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1
Xu, Changjin, and Peiluan Li. "Dynamics in a discrete predator-prey system with infected prey." Mathematica Bohemica 139, no. 3 (2014): 511–34. http://dx.doi.org/10.21136/mb.2014.143939.
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Schmitz, Oswald. "Predator and prey functional traits: understanding the adaptive machinery driving predator–prey interactions." F1000Research 6 (September 27, 2017): 1767. http://dx.doi.org/10.12688/f1000research.11813.1.
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Predator–prey relationships are a central component of community dynamics. Classic approaches have tried to understand and predict these relationships in terms of consumptive interactions between predator and prey species, but characterizing the interaction this way is insufficient to predict the complexity and context dependency inherent in predator–prey relationships. Recent approaches have begun to explore predator–prey relationships in terms of an evolutionary-ecological game in which predator and prey adapt to each other through reciprocal interactions involving context-dependent expression of functional traits that influence their biomechanics. Functional traits are defined as any morphological, behavioral, or physiological trait of an organism associated with a biotic interaction. Such traits include predator and prey body size, predator and prey personality, predator hunting mode, prey mobility, prey anti-predator behavior, and prey physiological stress. Here, I discuss recent advances in this functional trait approach. Evidence shows that the nature and strength of many interactions are dependent upon the relative magnitude of predator and prey functional traits. Moreover, trait responses can be triggered by non-consumptive predator–prey interactions elicited by responses of prey to risk of predation. These interactions in turn can have dynamic feedbacks that can change the context of the predator–prey interaction, causing predator and prey to adapt their traits—through phenotypically plastic or rapid evolutionary responses—and the nature of their interaction. Research shows that examining predator–prey interactions through the lens of an adaptive evolutionary-ecological game offers a foundation to explain variety in the nature and strength of predator–prey interactions observed in different ecological contexts.
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Clements, Hayley S., Craig J. Tambling, and Graham I. H. Kerley. "Prey morphology and predator sociality drive predator prey preferences." Journal of Mammalogy 97, no. 3 (2016): 919–27. http://dx.doi.org/10.1093/jmammal/gyw017.
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Yang, Wensheng, and Miqin Chen. "The Impact of Predator-dependent Prey Refuge on the Dynamics of a Leslie-Gower Predator-prey Model." Asian Research Journal of Mathematics 19, no. 11 (2023): 203–11. http://dx.doi.org/10.9734/arjom/2023/v19i11766.
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In this paper, we propose a new Leslie-Gower predator-prey model with predator-dependent prey refuge. Firstly, we obtain the positivity and boundedness of the system solution. Secondly, we prove that the origin is unstable using blow-up method, analyze the existence and local stability of the boundary equilibrium point and positive equilibrium point, and prove that the unique positive equilibrium point of the system is globally asymptotically stable by constructing a suitable Dulac function. Finally, mathematic analysis and numerical simulation show that: (1) when the strength of the predator-dependent prey refuge k = 0 , the dynamics of the predator-prey system without predator-dependent prey refuge are consistent with the results obtained from the traditional Leslie-Gower predator-prey system; (2) when k tends to positive infinity, the predator-dependent refuge lead to prey population densities fall somewhere between without prey refuge and with proportional refuge. However, the predator densities within this new form of the predator-dependent prey refuge is greater than the densities of predators without prey refuge and with proportional refuge; (3) increasing the strength k of the predator-dependent prey refuge can increase the densities of predator and prey populations respectively.
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Brown, Joel S., Keren Embar, Eric Hancock, and Burt P. Kotler. "Predators risk injury too: the evolution of derring-do in a predator–prey foraging game." Israel Journal of Ecology and Evolution 62, no. 3-4 (2016): 196–204. http://dx.doi.org/10.1080/15659801.2016.1207298.
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Derring-do is how aggressive a predator is in stalking and capturing prey. We model predator–prey interactions in which prey adjust vigilance behavior to mitigate risk of predation and predators their derring-do to manage risk of injury from capturing prey. High derring-do increases a predator's likelihood of capturing prey, but at higher risk of injury to itself. For fixed predator derring-do, prey increase vigilance in response to predator abundance, predator lethality, and predator encounter probability with prey and decrease vigilance with their own feeding rate; there is a humped-shaped relationship between prey vigilance and effectiveness of vigilance. For fixed prey vigilance, predators increase derring-do with the abundance of prey and predator lethality and decrease it with benefit of vigilance to prey and level of prey vigilance. When both prey and predator are behaviorally flexible, a predator–prey foraging game ensues whose solution represents an evolutionarily stable strategy (ESS). At the ESS, prey provide themselves with a public good as their vigilance causes predators to decrease derring-do. Conversely, predators have negative indirect effects on themselves as their derring-do causes prey to be more vigilant. These behavioral feedbacks create negative intra-specific interaction coefficients. Increasing the population size of prey (or predators) now has a direct negative effect on the prey (or predators). Both effects help stabilize predator–prey dynamics. Besides highlighting a common way by which predators may experience a food-safety tradeoff via dangerous prey, the model suggests why natural selection favors even small defensive measures by prey and hulky predators.
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Lemos, Walkymário Paulo, José Cola Zanuncio, and José Eduardo Serrão. "Attack behavior of Podisus rostralis (Heteroptera: Pentatomidade) adults on caterpillars of Bombyx mori (Lepidoptera: Bombycidae)." Brazilian Archives of Biology and Technology 48, no. 6 (2005): 975–81. http://dx.doi.org/10.1590/s1516-89132005000800014.
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Attack behavior of the predator Podisus rostralis (Stäl) (Heteroptera: Pentatomidae) adults on fourth instar Bombyx mori L. (Lepidoptera: Bombycidae) caterpillars was studied in laboratory conditions. Ten 24 hours old adults of this predator were observed during two hours with the following attack behavior: (1) Predator: prey finding; prey observation; touching prey with antenna; attack behavior; prey paralysis; predator retreat after attack; attack cessation; successive attacks; and (2) Prey: defense. The predator P. rostralis found its prey before attacking and it approached it with slow circular movements. The attack was usually made in the posterior part of the prey to reduce defense reaction. Larger size of prey in relation to the predator resulted difficult prey paralysis but it occurred in less than two hours.
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Chakraborty, Deep Chandan. "Dynamics of Predator-prey Interactions in Sharp Tooth Catfish (Clarias gariepinus; Burchell, 1822) and Carp Fingerlings (Labeo bata; Hamilton, 1822) with Special Reference to the Development of Anti-Predatory Strategies." UTTAR PRADESH JOURNAL OF ZOOLOGY 46, no. 1 (2025): 227–36. https://doi.org/10.56557/upjoz/2025/v46i14757.
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This study explores the dynamics of predator-prey interactions and functional response of Clarias gariepinus (African Magur/Sharptooth Catfish - predator) and of Labeo bata (Carp fingerlings - prey). Author investigated the behavioral patterns of both species in isolation and during encounters, exploring the impacts of predator size, prey-predator ratio, encounter duration and placement of separators on anti-predatory strategies. Results indicated that prey behavior is influenced by predator presence, with crowding, hiding, and inspection emerging as key anti-predatory strategies. The development and intensity of these strategies are intricately linked to prey-predator ratio, size difference, and encounter duration. Notably, larger predators trigger more pronounced anti-predatory responses in preys, while high prey composition motivates individuals to inspect predators, conveying fearlessness and fitness. Findings provide valuable insights into the evolution of predator-avoidance behaviors in prey species, sheds light on the complex dynamics governing predator-prey interactions in aquatic ecosystems.
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Nakazawa, Takefumi, Shin-ya Ohba, and Masayuki Ushio. "Predator–prey body size relationships when predators can consume prey larger than themselves." Biology Letters 9, no. 3 (2013): 20121193. http://dx.doi.org/10.1098/rsbl.2012.1193.
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As predator–prey interactions are inherently size-dependent, predator and prey body sizes are key to understanding their feeding relationships. To describe predator–prey size relationships (PPSRs) when predators can consume prey larger than themselves, we conducted field observations targeting three aquatic hemipteran bugs, and assessed their body masses and those of their prey for each hunting event. The data revealed that their PPSR varied with predator size and species identity, although the use of the averaged sizes masked these effects. Specifically, two predators had slightly decreased predator–prey mass ratios (PPMRs) during growth, whereas the other predator specialized on particular sizes of prey, thereby showing a clear positive size–PPMR relationship. We discussed how these patterns could be different from fish predators swallowing smaller prey whole.
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Troy, Maria Holmgren. "Predator and Prey." Edda 104, no. 02 (2017): 130–44. http://dx.doi.org/10.18261/issn.1500-1989-2017-02-04.
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Kraines, David P., and Vivian Y. Kraines. "Predator-Prey Model." College Mathematics Journal 22, no. 2 (1991): 160. http://dx.doi.org/10.2307/2686456.
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Agger, William A. "Predator and Prey." Annals of Internal Medicine 119, no. 6 (1993): 526. http://dx.doi.org/10.7326/0003-4819-119-6-199309150-00014.
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Mehlum, Halvor, Karl Moene, and Ragnar Torvik. "Predator or prey?" European Economic Review 47, no. 2 (2003): 275–94. http://dx.doi.org/10.1016/s0014-2921(01)00194-5.
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Tilahun, Surafel Luleseged. "Prey predator hyperheuristic." Applied Soft Computing 59 (October 2017): 104–14. http://dx.doi.org/10.1016/j.asoc.2017.04.044.
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Hoppensteadt, Frank. "Predator-prey model." Scholarpedia 1, no. 10 (2006): 1563. http://dx.doi.org/10.4249/scholarpedia.1563.
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Purdy, Laurence J. "Predator and Prey." JAMA: The Journal of the American Medical Association 263, no. 4 (1990): 523. http://dx.doi.org/10.1001/jama.1990.03440040062029.
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Taufiq, Irham, and Denik Agustito. "Model Predator-Prey dengan Dua Predator dan Satu Prey Terinfeksi." Indonesian Journal of Mathematics Education 1, no. 1 (2018): 8. http://dx.doi.org/10.31002/ijome.v1i1.887.
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<p>Di dalam penelitian ini, telah dibahas model matematika yang menunjukkan interaksi antara satu <em>prey</em> rentan dan <em>prey</em> terinfeksi dengan dua <em>predator</em>. Interaksi antara <em>predator</em> dan <em>prey</em> menggunakan fungsi respon Holling tipe II. Pertumbuhan <em>predator</em> dan <em>prey</em> menggunakan fungsi logistik. Dari model tersebut diperoleh delapan titik ekuilibrium. Kestabilan lokal masing-masing titik ekuilibrium dianalisis dengan metode linierisasi. Kemudian simulasi numerik menunjukan interaksi antara dua <em>predator</em>, <em>prey</em> rentan dan <em>prey</em> terinfeksi. </p>
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Takyi, Eric M., Kasey Cooper, Kya Jones, and Vincent T. Teyekpiti. "On Predator-Prey Dynamics: Incorporating Prey Vigilance and Predator Competition." Journal of Applied Nonlinear Dynamics 14, no. 3 (2025): 685–704. https://doi.org/10.5890/jand.2025.09.012.
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Putri, Riris Nur Patria, Windarto Windarto, and Cicik Alfiniyah. "Analisis Kestabilan Model Predator-Prey dengan Adanya Faktor Tempat Persembunyian Menggunakan Fungsi Respon Holling Tipe III." Contemporary Mathematics and Applications (ConMathA) 3, no. 2 (2021): 88. http://dx.doi.org/10.20473/conmatha.v3i2.30493.
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Predation is interaction between predator and prey, where predator preys prey. So predators can grow, develop, and reproduce. In order for prey to avoid predators, then prey needs a refuge. In this thesis, a predator-prey model with refuge factor using Holling type III response function which has three populations, i.e. prey population in the refuge, prey population outside the refuge, and predator population. From the model, three equilibrium points were obtained, those are extinction of the three populations which is unstable, while extinction of predator population and coexistence are asymptotic stable under certain conditions. The numerical simulation results show that refuge have an impact the survival of the prey.
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Fardinah, Fardinah. "Analisis Model Mangsa Pemangsa dengan Adanya Penyakit dan Pemanenan pada Pemangsa." Proximal: Jurnal Penelitian Matematika dan Pendidikan Matematika 6, no. 1 (2023): 122–29. http://dx.doi.org/10.30605/proximal.v6i1.2167.
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The interaction between two populations that are prey and predator can be described in a prey-predator model. In fact, in the interaction of prey and predators it can occur that when the density of prey is low, the effect of predation is also low, but if the size of the prey population increases, predation will be more intense which is stated in the Holling III Type response function model. In addition, it can also be found in an environment where there are populations of sick predator that result in death from the disease. This study aims to analyze the stability of the prey-predator model with the Holling III Type response function which consists of three subpopulations namely prey, healthy predator and sick predator. The analysis was carried out using the linearization method and then the type of stability was determined based on the characteristic eigenvalues obtained using the Routh-Hurwitz criteria. From this research it was found that population extinction is not possible while prey exists, extinction of diseased predator and populations exist is still possible if the required conditions are satisfy. Numerical simulations show that an increased harvesting rate in healthy predator populations results in a decrease in healthy predator populations, an increase in prey populations and a decrease in diseased predator populations. Meanwhile, a reduced harvesting rate for sick predator populations does not have a significant effect on the number of diseased predator populations, but results in an increase in the number of healthy predator populations and a decrease in prey populations
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Nugroho, Danar Agus, and Rina Reorita. "MODEL PREDATOR-PREY DENGAN DUA PREDATOR." Jurnal Ilmiah Matematika dan Pendidikan Matematika 5, no. 1 (2013): 43. http://dx.doi.org/10.20884/1.jmp.2013.5.1.2915.
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This paper discussed about the predator-prey model with two predators. This model is a development of the model given by Korobeinikov and Wake (1999). Dynamic behavior of the model can be determined based on the stability of the equilibrium point. The stability of the equilibrium point of predator-prey model with two predators on the general ecosystem shows that there is no coexistence state (grown in tandem) on both predators and for a long time one of the predators will lead to the local extinction even though there is no competition between the two predators. Furthermore, this model is applied to the brown plant hopper predator, mirid prey and tomcat prey. The result shows that the population of brown planthopper and both of the predators will oscillate towards a particular value with a shorter span of time. In the long term, the number of brown planthopper and mirid will be heading to the equilibrium point, while the tomcat will lead to local extinction.
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Cairns, Johannes, Felix Moerman, Emanuel A. Fronhofer, Florian Altermatt, and Teppo Hiltunen. "Evolution in interacting species alters predator life-history traits, behaviour and morphology in experimental microbial communities." Proceedings of the Royal Society B: Biological Sciences 287, no. 1928 (2020): 20200652. http://dx.doi.org/10.1098/rspb.2020.0652.
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Predator–prey interactions heavily influence the dynamics of many ecosystems. An increasing body of evidence suggests that rapid evolution and coevolution can alter these interactions, with important ecological implications, by acting on traits determining fitness, including reproduction, anti-predatory defence and foraging efficiency. However, most studies to date have focused only on evolution in the prey species, and the predator traits in (co)evolving systems remain poorly understood. Here, we investigated changes in predator traits after approximately 600 generations in a predator–prey (ciliate–bacteria) evolutionary experiment. Predators independently evolved on seven different prey species, allowing generalization of the predator's evolutionary response. We used highly resolved automated image analysis to quantify changes in predator life history, morphology and behaviour. Consistent with previous studies, we found that prey evolution impaired growth of the predator, although the effect depended on the prey species. By contrast, predator evolution did not cause a clear increase in predator growth when feeding on ancestral prey. However, predator evolution affected morphology and behaviour, increasing size, speed and directionality of movement, which have all been linked to higher prey search efficiency. These results show that in (co)evolving systems, predator adaptation can occur in traits relevant to foraging efficiency without translating into an increased ability of the predator to grow on the ancestral prey type.
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Sun, Xiaodan, Yingping Li, and Yanni Xiao. "A Predator–Prey Model with Prey Population Guided Anti-Predator Behavior." International Journal of Bifurcation and Chaos 27, no. 07 (2017): 1750099. http://dx.doi.org/10.1142/s0218127417500997.
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We consider a predator–prey system with prey population guided anti-predator behavior, in which anti-predator behaviors happen only when the population size of the prey is greater than a threshold. We investigate the rich dynamics of the proposed piecewise model as well as both subsystems without and with nonlinear functional response. In particular, the subsystem with anti-predator behaviors exhibits rich dynamical behaviors including saddle-node bifurcation, Hopf bifurcation, Bogdanov–Takens bifurcation and homoclinic bifurcation. Further, besides the dynamical properties of subsystems the piecewise system shows some new complicated dynamical behaviors as the threshold value varies, including unstable limit cycle, semistable limit cycle, bistability of equilibrium and limit cycle, and tristability of three equilibria. From the switching system we can conclude that a great anti-predator rate induces the prey population to persist more likely, but whether the prey and predator populations coexist depends further on the threshold that triggers anti-predator behavior. Especially, a large threshold not only makes coexistence of the prey and predator populations as an equilibrium more likely, but also damps the predator–prey oscillations.
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Lawson, Riley R., Dillon T. Fogarty, and Scott R. Loss. "Use of visual and olfactory sensory cues by an apex predator in deciduous forests." Canadian Journal of Zoology 97, no. 5 (2019): 488–94. http://dx.doi.org/10.1139/cjz-2018-0134.
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Predator–prey interactions influence behaviors and life-history evolution for both predator and prey species and also have implications for biodiversity conservation. A fundamental goal of ecology is to clarify mechanisms underlying predator–prey interactions and dynamics. To investigate the role of predator sensory mechanisms in predator–prey interactions, specifically in predator detection of prey, we experimentally evaluated importance of visual and olfactory cues for an apex predator, the coyote (Canis latrans Say, 1823). Unlike similar studies, we examined use of sensory cues in a field setting. We used trail cameras and four replicated treatments — visual only, olfactory only, visual and olfactory combined, and a control — to quantify coyote visitation rates in North American deciduous forests during fall 2016. Coyote visitation was greatest for olfactory-only and visual-only cues, followed by the combined olfactory–visual cue; all cues attracted more coyotes than the control (i.e., olfactory = visual > olfactory–visual > control). Our results suggest this apex predator uses both olfactory and visual cues while foraging for prey. These findings from a field study of free-roaming coyotes increase understanding of predator foraging behavior, predator–prey interactions, and sensory ecology. Our study also suggests future directions for field evaluations of the role of different sensory mechanisms in predator foraging and prey concealment behaviors.
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Kaitala, Veijo, Mikko Koivu-Jolma, and Jouni Laakso. "Infective prey leads to a partial role reversal in a predator-prey interaction." PLOS ONE 16, no. 9 (2021): e0249156. http://dx.doi.org/10.1371/journal.pone.0249156.
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An infective prey has the potential to infect, kill and consume its predator. Such a prey-predator relationship fundamentally differs from the predator-prey interaction because the prey can directly profit from the predator as a growth resource. Here we present a population dynamics model of partial role reversal in the predator-prey interaction of two species, the bottom dwelling marine deposit feeder sea cucumber Apostichopus japonicus and an important food source for the sea cucumber but potentially infective bacterium Vibrio splendidus. We analyse the effects of different parameters, e.g. infectivity and grazing rate, on the population sizes. We show that relative population sizes of the sea cucumber and V. Splendidus may switch with increasing infectivity. We also show that in the partial role reversal interaction the infective prey may benefit from the presence of the predator such that the population size may exceed the value of the carrying capacity of the prey in the absence of the predator. We also analysed the conditions for species extinction. The extinction of the prey, V. splendidus, may occur when its growth rate is low, or in the absence of infectivity. The extinction of the predator, A. japonicus, may follow if either the infectivity of the prey is high or a moderately infective prey is abundant. We conclude that partial role reversal is an undervalued subject in predator-prey studies.
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Saha, Sangeeta, and Guruprasad Samanta. "Modelling of a two prey and one predator system with switching effect." Computational and Mathematical Biophysics 9, no. 1 (2021): 90–113. http://dx.doi.org/10.1515/cmb-2020-0120.
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Abstract Prey switching strategy is adopted by a predator when they are provided with more than one prey and predator prefers to consume one prey over others. Though switching may occur due to various reasons such as scarcity of preferable prey or risk in hunting the abundant prey. In this work, we have proposed a prey-predator system with a particular type of switching functional response where a predator feeds on two types of prey but it switches from one prey to another when a particular prey population becomes lower. The ratio of consumption becomes significantly higher in the presence of prey switching for an increasing ratio of prey population which satisfies Murdoch’s condition [15]. The analysis reveals that two prey species can coexist as a stable state in absence of predator but a single prey-predator situation cannot be a steady state. Moreover, all the population can coexist only under certain restrictions. We get bistability for a certain range of predation rate for first prey population. Moreover, varying the mortality rate of the predator, an oscillating system can be obtained through Hopf bifurcation. Also, the predation rate for the first prey can turn a steady-state into an oscillating system. Except for Hopf bifurcation, some other local bifurcations also have been studied here. The figures in the numerical simulation have depicted that, if there is a lesser number of one prey present in a system, then with time, switching to the other prey, in fact, increases the predator population significantly.
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Rahmawati, Ruli, and Dian Savitri. "Model Lotka-Volterra yang Mempertimbangkan Efek Ketakutan pada Prey dengan Fungsi Respon Holling Tipe II." MATHunesa: Jurnal Ilmiah Matematika 11, no. 2 (2023): 304–9. http://dx.doi.org/10.26740/mathunesa.v11n2.p304-309.
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Interaksi antar populasi pada ekosistem sawah antara burung hantu (Tyto alba) dengan tikus sawah (Rattus argentiventer) direpresentasikan sebagai model predator-prey yang mempertimbangkan efek ketakutan. Interaksi dua populasi ini menggunakan fungsi respon Holling tipe II. Model predator-prey ini dikonstruksi berdasarkan asumsi perilaku prey yaitu tikus sawah yang memiliki efek ketakutan terhadap predator burung hantu. Berdasarkan beberapa jurnal rujukan yang dikembangkan dengan pola pemangsaan menggunakan fungsi respon Holling tipe II. Analisis perhitungan pada penelitian ini dilakukan dengan mencari titik kesetimbangan dan analisis kestabilan. Hasil analisis didapatkan titik kesetimbangan , , dan dengan A = > 0, B = , C = . Hasil analisis kestabilan didapatkan titik E0 = (0,0) tidak stabil, E1 = ( ,0) stabil dengan syarat artinya kepunahan populasi predator terjadi saat konversi biomassa prey ke predator lebih besar dari kompetisi intra spesies prey, titik dan stabil dengan syarat g > µ artinya populasi prey dan predator tetap ada saat konversi biomassa prey ke predator lebih dari kematian alami predator. Simulasi numerik dilakukan untuk mengetahui kesesuaian hasil analisis dengan menggunakan aplikasi Phyton. Hasil simulasi numerik terhadap solusi sistem didapatkan konversi biomassa prey ke predator dengan berpengaruh pada kestabilan kedua populasi.
 Kata Kunci: Lotka-Volterra, efek ketakutan, Holling II.
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Belgrad, Benjamin A., and Blaine D. Griffen. "Predator–prey interactions mediated by prey personality and predator hunting mode." Proceedings of the Royal Society B: Biological Sciences 283, no. 1828 (2016): 20160408. http://dx.doi.org/10.1098/rspb.2016.0408.
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Predator–prey interactions are important drivers in structuring ecological communities. However, despite widespread acknowledgement that individual behaviours and predator species regulate ecological processes, studies have yet to incorporate individual behavioural variations in a multipredator system. We quantified a prevalent predator avoidance behaviour to examine the simultaneous roles of prey personality and predator hunting mode in governing predator–prey interactions. Mud crabs, Panopeus herbstii , reduce their activity levels and increase their refuge use in the presence of predator cues. We measured mud crab mortality and consistent individual variations in the strength of this predator avoidance behaviour in the presence of predatory blue crabs, Callinectes sapidus , and toadfish, Opsanus tau . We found that prey personality and predator species significantly interacted to affect mortality with blue crabs primarily consuming bold mud crabs and toadfish preferentially selecting shy crabs. Additionally, the strength of the predator avoidance behaviour depended upon the predation risk from the predator species. Consequently, the personality composition of populations and predator hunting mode may be valuable predictors of both direct and indirect predator–prey interaction strength. These findings support theories postulating mechanisms for maintaining intraspecies diversity and have broad implications for community dynamics.
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Mahmudah, Wilda, and Mohammad Rifai. "Analisis Kestabilan Model Prey-Predator dengan Penambahan Makanan Alternatif dan Fungsi Respon Holling Tipe III." Buana Matematika : Jurnal Ilmiah Matematika dan Pendidikan Matematika 10, no. 2 (2020): 133–46. http://dx.doi.org/10.36456/buanamatematika.v10i2.2728.
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Model prey-predator merupakan model interaksi dan pola perilaku antara dua spesies. Hubungan interaksi tersebut dinyatakan dalam bentuk model sistem dinamik atau persamaan differesial yang bergantung pada waktu. Pada kenyataan di lapangan predator sering mencari mangsa lain ketika jumlah mangsa yang biasa dimakannya menurun, sehingga perlu adanya penambahan makanan alternatif dan juga fungsi respon Holling pada model prey-predator yang ada. Pada penelitian ini, dilakukan analisis kestabilan pada model sistem prey-predator dengan penambahan makanan alternatif dan fungsi respon holling tipe III. Tujuan dari penelitian ini adalah untuk mengetahui bagaimana kestabilan pada sistem tersebut. Prosedur penelitian ini adalah studi literatur, merekonstruksi pembentukan model prey-predator, menentukan titik kesetimbangan, menentukan kestabilan dititik kesetimbangan, mensimulasikan sistem prey-predator, dan penarikan kesimpulan. Dari hasil analisis didapatkan tiga titik kesetimbangan yaitu kepunahan prey-predator(E0), kepunahan predator (E1) dan prey-predator saling berinteraksi atau hidup bersama(E2). Pada titik kesetimbangan E0 bersifat tidak stabil, sedangkan pada E1 dan E2 bersifat stabil asimtotis dengan syarat batas tertentu. Hasil simulasi numerik juga menunjukkan bahwa stabilitas yang ditunjukkan untuk ketiga titik kesetimbangan juga memberikan hasil yang sama dengan hasil analitik.
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Gibert, Jean P., and John P. DeLong. "Temperature alters food web body-size structure." Biology Letters 10, no. 8 (2014): 20140473. http://dx.doi.org/10.1098/rsbl.2014.0473.
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The increased temperature associated with climate change may have important effects on body size and predator–prey interactions. The consequences of these effects for food web structure are unclear because the relationships between temperature and aspects of food web structure such as predator–prey body-size relationships are unknown. Here, we use the largest reported dataset for marine predator–prey interactions to assess how temperature affects predator–prey body-size relationships among different habitats ranging from the tropics to the poles. We found that prey size selection depends on predator body size, temperature and the interaction between the two. Our results indicate that (i) predator–prey body-size ratios decrease with predator size at below-average temperatures and increase with predator size at above-average temperatures, and (ii) that the effect of temperature on predator–prey body-size structure will be stronger at small and large body sizes and relatively weak at intermediate sizes. This systematic interaction may help to simplify forecasting the potentially complex consequences of warming on interaction strengths and food web stability.
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Sih, Andrew. "Prey refuges and predator-prey stability." Theoretical Population Biology 31, no. 1 (1987): 1–12. http://dx.doi.org/10.1016/0040-5809(87)90019-0.
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Khadijah, Mustika, Yuni Yulida, and Dewi Sri Susanti. "MODEL MANGSA-PEMANGSA DENGAN FUNGSI RESPON HOLLING DAN PEMANENAN." EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN 15, no. 2 (2022): 93. http://dx.doi.org/10.20527/epsilon.v15i2.4593.
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The mathematical model of prey-predator interaction is one of the stages of solving mathematical problems by simplifying events that occur in mathematical form. In this research, we discuss a prey-predator model using a type II Holling response function without harvesting and a prey-predator model using a type II Holling response function with harvesting. The purpose of this research was to explain the formation of a prey-predator model with a type II Holling response and a preypredator model with a type II Holling response with harvesting, to determine the stability at the equilibrium point of the model, and to create a model simulation using several sample parameters. The results obtained were three equilibrium points for the prey-predator model with type II Holling response without harvesting and two equilibrium points for the prey-predator model with type II Holling response with harvesting. The stability at two equilibrium points of the prey-predator model using the type II Holling response function without harvesting was asymptotically stable and the stability at one equilibrium point in the prey-predator model using the type II Holling response function in the presence of harvesting in the prey population was asymptotically stable. The comparison of numerical simulations showed that the number of predator population without harvesting was greater than the number of predator population with harvesting.
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Walzer, Andreas, and Peter Schausberger. "Integration of multiple cues allows threat-sensitive anti-intraguild predator responses in predatory mites." Behaviour 150, no. 2 (2013): 115–32. http://dx.doi.org/10.1163/1568539x-00003040.
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Intraguild (IG) prey is commonly confronted with multiple IG predator species. However, the IG predation (IGP) risk for prey is not only dependent on the predator species, but also on inherent (intraspecific) characteristics of a given IG predator such as its life-stage, sex or gravidity and the associated prey needs. Thus, IG prey should have evolved the ability to integrate multiple IG predator cues, which should allow both inter- and intraspecific threat-sensitive anti-predator responses. Using a guild of plant-inhabiting predatory mites sharing spider mites as prey, we evaluated the effects of single and combined cues (eggs and/or chemical traces left by a predator female on the substrate) of the low risk IG predator Neoseiulus californicus and the high risk IG predator Amblyseius andersoni on time, distance and path shape parameters of the larval IG prey Phytoseiulus persimilis. IG prey discriminated between traces of the low and high risk IG predator, with and without additional presence of their eggs, indicating interspecific threat-sensitivity. The behavioural changes were manifest in distance moved, activity and path shape of IG prey. The cue combination of traces and eggs of the IG predators conveyed other information than each cue alone, allowing intraspecific threat-sensitive responses by IG prey apparent in changed velocities and distances moved. We argue that graded responses to single and combined IG predator cues are adaptive due to minimization of acceptance errors in IG prey decision making.
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M.F. Alhegazi, Zainb, and Hanan amhimmid Ali amhimmid. "On Stability Properties In Prey-Prodator Model With General Incidence." المجلة الليبية العالمية, no. 66 (June 17, 2024): 1–10. http://dx.doi.org/10.37376/glj.vi66.5890.
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In this paper we consider a prey-predator systems that the susceptibleand infected prey population are predated by predator species .Also we discuss different models of prey-predator systems With general incidence H ( S,I)The aim of this paper is to study the dynamic of prey-predator model by different techniques with a generalized incidence .
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Zhang, Hui, Zhihui Ma, Gongnan Xie, and Lukun Jia. "Effects of Behavioral Tactics of Predators on Dynamics of a Predator-Prey System." Advances in Mathematical Physics 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/375236.
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A predator-prey model incorporating individual behavior is presented, where the predator-prey interaction is described by a classical Lotka-Volterra model with self-limiting prey; predators can use the behavioral tactics of rock-paper-scissors to dispute a prey when they meet. The predator behavioral change is described by replicator equations, a game dynamic model at the fast time scale, whereas predator-prey interactions are assumed acting at a relatively slow time scale. Aggregation approach is applied to combine the two time scales into a single one. The analytical results show that predators have an equal probability to adopt three strategies at the stable state of the predator-prey interaction system. The diversification tactics taking by predator population benefits the survival of the predator population itself, more importantly, it also maintains the stability of the predator-prey system. Explicitly, immediate contest behavior of predators can promote density of the predator population and keep the preys at a lower density. However, a large cost of fighting will cause not only the density of predators to be lower but also preys to be higher, which may even lead to extinction of the predator populations.
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Fardinah, Darma Ekawati, Hikmah Hikmah, and Hirman Rachman. "Model Predator-Prey Leslie-Gower dengan Fungsi Respon Sokol-Howell dan Perilaku Anti Predator." Journal of Mathematics: Theory and Applications 6, no. 1 (2024): 19–30. http://dx.doi.org/10.31605/jomta.v6i1.2971.
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This study discusses the Leslie-Gower predator-prey model with the Sokol-Howell response function and anti-predator behavior. It is assumed that prey has anti-predator behavior that aims to reduce the risk of predation and not as an attempt by prey to find food. This study aims to formulate a Leslie-Gower predator-prey model with the Sokol-Howell response function and anti-predator behavior, analyze the model's equilibrium point and model interpretation. Stability analysis was carried out using the linearization method. The type of stability is determined based on the characteristic eigenvalues obtained using Routh-Hurwitz criteria. The results of the analysis of the equilibrium point show that prey populations will exist and predators will become extinct if the anti-predator coefficient is greater than the intrinsic growth coefficient of predators, while prey and predator populations will always exist if the intrinsic growth coefficient of predators is greater than the anti-predator coefficient and fulfills other conditions required. Based on the numerical simulations performed, the interpretation is that an enlarged anti-predator coefficient increases the number of prey populations until they approach the carrying capacity, while predator populations decrease significantly and over time experience extinction.
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Kisoma, Linus Nyarusanda. "Modelling Seasonal Migration Patterns of Wildebeest under Climate-Driven Changes: A Predator-Prey Model with De Angelis Functional Response." Asian Research Journal of Mathematics 21, no. 2 (2025): 23–34. https://doi.org/10.9734/arjom/2025/v21i2890.
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This study models the dynamics of a predator-prey system influenced by seasonal resource availability and prey migration. A two-dimensional spatial model simulates prey and predator populations, where prey growth is driven by seasonal resource fluctuations, and migration is guided by the spatial distribution of resources. The results show that higher resources during the wet season leads to increased prey density and migration, while lower resources in the dry season reduce prey growth and movement. Predator populations follow prey density changes, with a delayed increase in response to prey population peaks. Overall, the model highlights the critical role of seasonal resource variability in shaping predator-prey interactions and migration patterns.
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Dwi Putra, M. Adib Jauhari, and Ade Ima Afifa Himayati. "Stability Analysis of Leslie-Gower Model with Herd Behavior on Prey." InPrime: Indonesian Journal of Pure and Applied Mathematics 4, no. 1 (2022): 65–71. http://dx.doi.org/10.15408/inprime.v4i1.24464.
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AbstractWe studied the Leslie-Gower model of predator-prey with herd behavior. The square root functional response models predator and prey interactions that show herd behavior. This study aims to determine the formulation of the predator-prey model with herd behavior on prey, knowing the fixed points and its stability and simulating the model numerically. We found three fixed points that may exist: the extinction point of both species, the extinction of predator point, and the point of coexistence of the two species. The extinction of predator points is always unstable, while the point of coexistence of the two species can be stable under certain conditions. Due to the presence of square roots, the behavior of the solutions near the extinction point of the two species is not readily apparent. Numeric simulation shows that changing the initial condition and parameters can change the system's stability.Keywords: predator-prey; functional response; herd behavior; square root functional response, Leslie-Gower model. AbstrakArtikel membahas model predator prey Leslie-Gower dengan perilaku bergerombol pada prey. Interaksi predator dan prey yang menunjukkan perilaku bergerombol dimodelkan dengan fungsi respon akar kuadrat. Penelitian ini bertujuan untuk mengetahui formulasi model predator-prey dengan perilaku bergerombol pada prey, mengetahui titik ekuilibrium dan kestabilannya serta menyimulasikan model tersebut secara numerik. Hasil menunjukkan terdapat tiga titik tetap yang mungkin eksis, yaitu titik kepunahan kedua spesies, titik kepunahan predator dan titik koeksistensi kedua spesies. Titik kepunahan predator selalu tidak stabil, sedangkan titik koeksistensi kedua spesies bisa stabil dengan syarat tertentu. Karena adanya akar kuadrat, perilaku solusi di dekat titik kepunahan kedua spesies tidak mudah terlihat. Simulasi numerik menunjukkan bahwa perubahan nilai awal dan parameter dapat mengubah kestabilan sistem.Kata Kunci: predator prey; fungsi respons; perilaku bergerombol; fungsi respon akar kuadrat; model Leslie-Gower.
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Fitria, Vivi Aida. "Analisis Sistem Persamaan Diferensial Model Predator-prey dengan Perlambatan." CAUCHY 2, no. 1 (2011): 41. http://dx.doi.org/10.18860/ca.v2i1.1807.
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<div class="standard"><a id="magicparlabel-2437">Model predator-prey dengan perlambatan merupakan model interaksi dua spesies antara mangsa dan pemangsa yang berbentuk sistem persamaan diferensial tak liner. Adanya waktu perlambatan sangat mempengaruhi kestabilan titik ekuilibrium sistem persamaan diferensial model predator-prey. Penelitian ini bertujuan untuk menganalisis pengaruh waktu perlambatan terhadap kestabilan titik ekuilibrium sistem persamaan diferensial model predator-prey. Namun sebelum itu, agar dapat diketahui asal mula pembentukan model predator-prey dengan perlambatan akan dianalisis proses terbentuknya model predator-prey dengan perlambatan. Penelitian ini menggunakan penelitian kepustakaan, yaitu dengan menampilkan argumentasi penalaran keilmuan yang memaparkan hasil kajian literatur dan hasil olah pikir peneliti mengenai suatu permasalahan atau topik kajian. Hasil penelitian ini menunjukkan bahwa ada beberapa nilai perlambatan yang menyebabkan titik ekuilibrium sistem persamaan diferensial model predator-prey stabil, dan ada beberapa nilai perlambatan yang menyebabkan titik ekuilibrium sistem persamaan diferensial model predator-prey tidak stabil.</a></div>
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Mata, Cristina, Jesús Herranz, and Juan E. Malo. "Attraction and Avoidance between Predators and Prey at Wildlife Crossings on Roads." Diversity 12, no. 4 (2020): 166. http://dx.doi.org/10.3390/d12040166.
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Wildlife passages are currently built at roads and railway lines to re-establish connectivity. However, little is known about whether predator-prey interactions may reduce the effectiveness of the crossing structures. We evaluated the co-occurrence patterns of predator-prey species-pairs at 113 crossing structures, noting their coincidence at the same structure and/or on the same day. We built occupancy models using presence-absence matrices for three prey and five predator types obtained during 2076 passage-days of monitoring. The results indicate that predators and prey do not use passages independently. Attraction or segregation effects occurred in 20% of predator-prey species-pairs and were detected in 67% of cases with respect to same-day use. Our results show that both predator and prey species used the same structures to cross fenced roads. However, the spatial and daily patterns of crossing suggest that there were predators that attended crossings to search for prey and that prey species avoided using crossings in the presence of predators. Our results support two recommendations to avoid crossing structures losing effectiveness or becoming prey traps: (i) increase the number of wider structures to reduce the risks of predator-prey encounters and (ii) include inside them structural heterogeneity and refuges, to reduce the likelihood for predator-prey interactions.
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SHOLIHAH, TYAN HIDAYATUS. "MODEL MATEMATIKA MANGSA PEMANGSA TIGA SPESIES DENGAN FUNGSI RESPON HOLLING TIPE II DAN HOLLING TIPE IV SERTA PEMANENAN PADA POPULASI MANGSA." MATHunesa: Jurnal Ilmiah Matematika 8, no. 2 (2020): 168–73. http://dx.doi.org/10.26740/mathunesa.v8n2.p168-173.
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In this world, living things are interdependent. Every living creature needs another living creature, so there is an interaction between the two. One of interactions that occur in mini style is predator prey interaction. The interaction of prey and predator in the world of ecology is an important and interesting thing to discuss. Therefore many researchers make mathematical models of predator prey to find out the interacions of these prey predators. In this study involved three species, namely two species of prey and one species of predator. Concerning predatory prey behavior with Holling type II, and Holling type IV response functions and harvesting in second prey populations. In this study, the type IV Holling function is used when the predator preys on the first prey, and the type II Holling response function is used when the predator preys on the second prey. This research is a type of quantitative research that examines theories and concepts relating to the problems discussed in this study through various literature sources. This article specifically discusses concerning the construction of predator prey models with Holling type II, and Holling type IV response functions as well as harvesting in the second prey population models obtained from the results of construction in this study are in equation (21).
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Juanes, Francis. "A length-based approach to predator–prey relationships in marine predators." Canadian Journal of Fisheries and Aquatic Sciences 73, no. 4 (2016): 677–84. http://dx.doi.org/10.1139/cjfas-2015-0159.
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Body size is a critical feature of the ecology of most organisms and has been used to describe and understand predator–prey interactions in both terrestrial and aquatic environments. Most previous studies have used prey mass to examine the relationships between predator size and prey size; however, using prey lengths may provide a different perspective, particularly for gape-limited fishes. Using a large database of predator and prey lengths for marine aquatic predators, I found the expected positive wedge-shaped relationship between predator length and prey length and a negative converging relationship between relative prey length (prey–predator length ratio = a measure of trophic niche breadth) and predator length. Distinct patterns in the size scaling of this measure of trophic niche breadth were identified using quantile regression: converging relationships were common among adults but absent among larvae. This difference suggests contrasting ontogenetic foraging opportunities between adults and larvae: a lack of large relative prey sizes for the largest adult predators, and a greater ability of larvae to include larger prey items in their diet as they grow.
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Liu, Lingyu, Xiaobo Li, and Pengcheng Li. "Dynamics for a Ratio-Dependent Prey–Predator Model with Different Free Boundaries." Mathematics 12, no. 12 (2024): 1897. http://dx.doi.org/10.3390/math12121897.
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In this paper, we study the dynamics of the ratio-dependent type prey–predator model with different free boundaries. The two free boundaries, determined by prey and predator, respectively, implying that they may intersect with each other as time evolves, are used to describe the spreading of prey and predator. Our primary focus lies in analyzing the long-term behaviors of both predator and prey. We establish sufficient conditions for the spreading and vanishing of prey and predator. Furthermore, in cases where spread occurs, we offer estimates for the asymptotic spreading speeds of prey and predator, denoted as u and v, respectively, as well as the asymptotic speeds of the free boundaries, denoted by h and g. Our findings reveal that when the predator’s speed is lower than that of the prey, it leads to a reduction in the prey’s asymptotic speed.
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Guzman, Laura Melissa, and Diane S. Srivastava. "Prey body mass and richness underlie the persistence of a top predator." Proceedings of the Royal Society B: Biological Sciences 286, no. 1902 (2019): 20190622. http://dx.doi.org/10.1098/rspb.2019.0622.
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Predators and prey often differ in body mass. The ratio of predator to prey body mass influences the predator's functional response (how consumption varies with prey density), and therefore, the strength and stability of the predator–prey interaction. The persistence of food chains is maximized when prey species are neither too big nor too small relative to their predator. Nonetheless, we do not know if (i) food web persistence requires that all predator–prey body mass ratios are intermediate, nor (ii) if this constraint depends on prey diversity. We experimentally quantified the functional response for a single predator consuming prey species of different body masses. We used the resultant allometric functional response to parametrize a food web model. We found that predator persistence was maximized when the minimum prey size in the community was intermediate, but as prey diversity increased, the minimum body size could take a broader range of values. This last result occurs because of Jensen's inequality: the average handling time for multiple prey of different sizes is higher than the handling time of the average sized prey. Our results demonstrate that prey diversity mediates how differences between predators and prey in body mass determine food web stability.
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Lundvall, David, Richard Svanbäck, Lennart Persson, and Pär Byström. "Size-dependent predation in piscivores: interactions between predator foraging and prey avoidance abilities." Canadian Journal of Fisheries and Aquatic Sciences 56, no. 7 (1999): 1285–92. http://dx.doi.org/10.1139/f99-058.
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Body size is known to play a crucial role in predator-prey interactions. For a given predator size, it has been suggested that prey mortality should be a dome-shaped function dependent on prey body size. In this study, we experimentally tested (i) the suggested mechanisms responsible for the dome-shaped prey vulnerability function and (ii) whether a prey refuge affected the form of this function. As prey, we used young-of-the-year Eurasian perch (Perca fluviatilis), and as predator, larger Eurasian perch. The prey mortality as a function of prey size was dome shaped for large and medium predators but decreased monotonically with prey size for small predators. Capture success of predators decreased monotonically with increasing prey size and was lower for small predators. In refuge trials, the mortality of prey declined monotonically with prey size for all predator sizes. Refuge use of prey increased with the sizes of both prey and predator. Our results suggest that the hypothesized dome-shaped relationship on prey vulnerability can be altered by the presence of an absolute prey refuge. Our results further suggest that the ability to perform more flexible foraging behaviors is of increasing importance when prey size increases.
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Abdul Manaf, Zati Iwani, and Mohd Hafiz Mohd. "The Effects of Varying Predator Dispersal Strength on Prey-Predator Dynamics with Refuge Process." Malaysian Journal of Fundamental and Applied Sciences 19, no. 5 (2023): 791–803. http://dx.doi.org/10.11113/mjfas.v19n5.3088.
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The combined effects of (symmetric or asymmetric) dispersal and refuge mechanisms can have a significant impact on prey-predator dynamics. However, there remains a knowledge gap in concerning the incorporation of asymmetrical dispersal in the presence of prey refuges. Therefore, this paper aims to examine the influence of varying levels of asymmetrical (i.e., predator) dispersal on the interactions between prey and predators, as well as the role of prey refuges in facilitating species coexistence. The investigation begins by introducing an ordinary differential equation (ODE) model for the prey-predator system, which is subsequently extended to a partial differential equation (PDE) model. By conducting one-parameter bifurcation analysis on both models, the presence of transcritical and Hopf bifurcation points is established. Furthermore, the research delves into the spatio-temporal dynamics of the PDE model, capturing the intricate interactions between a specialized prey species and its predator. The focus is on examining the effects of different strengths of predator dispersal on the dynamics of the prey-predator system. The aim is to gain a comprehensive understanding of how predator dispersal influences the stability and persistence of the system, and to investigate the ecological implications of these dynamics in terms of prey-predator coexistence. Hence, the main findings of the research suggest that the increased levels of predator dispersal led to a wider range of prey refuges, supporting species coexistence. In conclusion, this study emphasises the critical importance of predator and prey dispersal dynamics in determining the key mechanisms that can promote species coexistence
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Belew, Basaznew, and Dawit Melese. "Modeling and Analysis of Predator-Prey Model with Fear Effect in Prey and Hunting Cooperation among Predators and Harvesting." Journal of Applied Mathematics 2022 (December 3, 2022): 1–14. http://dx.doi.org/10.1155/2022/2776698.
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In this paper, we present and analyze predator-prey system where prey population is linearly harvested and affected by fear and the prey population has grown logistically in the absence of predators. The predator population follows hunting cooperation, and it predates the prey population in the Holling type II functional responses. Based on those assumptions, a two-dimensional mathematical model is derived. The positivity, boundedness, and extinction of both prey and predator populations of the solution of the system are discussed. The existence, stability (local and global), and the Hopf bifurcation analysis of the biologically feasible equilibrium points are investigated. The aim of this research is to explore the effect of fear on the prey population and hunting cooperation on the predator population, and both prey and predator populations are harvested linearly and taken as control parameters of the model. If the values of c 1 > 1 , then both prey and predator populations are extinct and also fear parameter has a stabilizing effect on system 4. From the numerical simulation, it was found that the fear effect, hunting cooperation, prey harvesting, and predator harvesting change the dynamics of system 4.
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Floeter, Jens, and Axel Temming. "Analysis of prey size preference of North Sea whiting, saithe, and grey gurnard." ICES Journal of Marine Science 62, no. 5 (2005): 897–907. http://dx.doi.org/10.1016/j.icesjms.2005.03.004.
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Abstract Size preference for prey fish of North Sea whiting, saithe, and grey gurnard was analysed. The analysis combined size-specific prey abundance estimates derived from bottom-trawl surveys with size frequencies of prey in predator stomachs from the International North Sea Stomach Database. To estimate the abundance of all potential prey fish in the sea, predator-specific length-based number spectra were calculated. Prey spectra were weighted by local predator abundance to take the spatial–temporal overlap between predator and their prey into consideration. Species-specific prey size preference models are presented. Contrary to former results, the preferred predator–prey weight ratio of whiting and grey gurnard is an exponentially increasing function of predator size and an exponentially decreasing function of the slope of the number spectrum. When predators grow, they prefer larger prey in absolute units. However, from a species-specific body size onwards they increasingly shift their prey preference towards relatively smaller prey sizes. From a bioenergetic point of view, this behaviour most likely maximizes the predator's foraging efficiency by reducing the expenditure of costly, anaerobically generated energy expended during burst swimming.
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Ah, Nurul Imamah, Wuryansari Muharini Kusumawinahyu, Agus Suryanto, and Trisilowati Trisilowati. "The Dynamics of a Predator-Prey Model Involving Disease Spread In Prey and Predator Cannibalism." Jambura Journal of Biomathematics (JJBM) 4, no. 2 (2023): 119–25. http://dx.doi.org/10.37905/jjbm.v4i2.21495.
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In this article, dynamics of predator prey model with infection spread in prey and cannibalism in predator is analyzed. The model has three populations, namely susceptible prey, infected prey, and predator. It is assumed that there is no migration in both prey and predator populations. The dynamical analysis shows that the model has six equilibria, namely the trivial equilibrium point, the prey extinction point, the disease free and predator extinction equilibrium point, the disease-free equilibrium point, the predator extinction equilibrium point, and the coexistence equilibrium point. The first equilibrium is unstable, and the other equilibria conditionally local asymptotically stable. The positivity and boundedness of the solution are also shown. The analytical result is supported by numerical simulation. It is shown that in such a high cannibalization the coexistence equilibrium is locally asymptotically stable.
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Huang, Xuming, Xiangzeng Kong, and Wensheng Yang. "Permanence of Periodic Predator-Prey System with General Nonlinear Functional Response and Stage Structure for Both Predator and Prey." Abstract and Applied Analysis 2009 (2009): 1–8. http://dx.doi.org/10.1155/2009/481712.
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We study the permanence of periodic predator-prey system with general nonlinear functional responses and stage structure for both predator and prey and obtain that the predator and the prey species are permanent.
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Luo, Yantao, Long Zhang, Zhidong Teng, and Tingting Zheng. "Coexistence for an Almost Periodic Predator-Prey Model with Intermittent Predation Driven by Discontinuous Prey Dispersal." Discrete Dynamics in Nature and Society 2017 (2017): 1–15. http://dx.doi.org/10.1155/2017/7037245.
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An almost periodic predator-prey model with intermittent predation and prey discontinuous dispersal is studied in this paper, which differs from the classical continuous and impulsive dispersal predator-prey models. The intermittent predation behavior of the predator species only happens in the channels between two patches where the discontinuous migration movement of the prey species occurs. Using analytic approaches and comparison theorems of the impulsive differential equations, sufficient criteria on the boundedness, permanence, and coexistence for this system are established. Finally, numerical simulations demonstrate that, for an intermittent predator-prey model, both the intermittent predation and intrinsic growth rates of the prey and predator species can greatly impact the permanence, extinction, and coexistence of the population.