Log in

Relevant bibliographies by topics / Holling type IV functional response / Journal articles

To see the other types of publications on this topic, follow the link: Holling type IV functional response.

Journal articles on the topic 'Holling type IV functional response'

Author: Grafiati

Published: 4 June 2025

Last updated: 8 July 2025

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Holling type IV functional response.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Hama, Mudhafar Fattah. "Dynamics of SVIS Model with Holling Type IV Functional Response." JOURNAL OF ADVANCES IN MATHEMATICS 11, no. 10 (2016): 5752–65. http://dx.doi.org/10.24297/jam.v11i10.804.

Full text

Abstract:

In this paper, we will study the effect of some epidemic concepts such as immigrants and vaccine on the dynamical behaviour of epidemic models. The existence, uniqueness and boundedness of the solution are investigated. The local stability analyses of the system is carried out .The global dynamics of the system is investigated numerically.

APA, Harvard, Vancouver, ISO, and other styles

2

Rouzimaimaiti, Mahemuti, and Ablimit Akbar. "Permanence and extinction for a delayed periodic predator-prey system." Journal of Progressive Research in Mathematics 1, no. 1 (2015): 23–35. https://doi.org/10.5281/zenodo.3980863.

Full text

Abstract:

In this paper, the permanence, extinction and periodic solution of a delayed periodic predator-prey system with Holling type IV functional response and stage structure for prey is studied. By means of comparison theorem, some sufficient and necessary conditions are derived for the permanence of the system.

APA, Harvard, Vancouver, ISO, and other styles

3

Jiao, Yu Juan. "Global Solutions of a Diffusive Predator-Prey Model with Holling IV Functional Response." Applied Mechanics and Materials 336-338 (July 2013): 664–67. http://dx.doi.org/10.4028/www.scientific.net/amm.336-338.664.

Full text

Abstract:

Using the energy estimates and Gagliardo-Nirenberg type inequalities, the uniform boundedness and global existence of solutions for a predator-prey model with Holling IV functional response with self- and cross-diffusion are proved.

APA, Harvard, Vancouver, ISO, and other styles

4

Ghosh, Partha, Pritha Das, and Debasis Mukherjee. "Chaos to order — Effect of random predation in a Holling type IV tri-trophic food chain system with closure terms." International Journal of Biomathematics 09, no. 05 (2016): 1650073. http://dx.doi.org/10.1142/s179352451650073x.

Full text

Abstract:

Complex dynamics of modified Hastings–Powell (HP) model (phytoplankton-zoo-plankton-fish) with Holling type IV functional response and density-dependent mortality (closure terms) for top predator species is investigated in this paper. Closure terms describe the mortality of top predator in plankton food chain models. Modified HP model with Holling type IV functional response gives rise to similar type of chaotic dynamics (inverted “teacup attractor”) as observed in original HP model with Holling type II functional response. It is observed that introduction of nonlinear closure terms eliminate chaos and system dynamics becomes stable. Observation of this paper support the “Steele–Henderson conjecture” that, nonlinear closure terms eliminate or reduces limit cycles and chaos in plankton food chain models. Chaotic or stable dynamics are numerically verified by Lyapunov exponents (LE) method and Sil’nikov eigenvalue analysis and also illustrated graphically by plotting bifurcation diagrams. It is assumed that mortality of fish population, caused by higher-order predators (which are not explicitly included in the model) is not constant, rather it exhibits random variation throughout the year. To incorporate the effect of random mortality of fish population, white noise term is introduced into the original deterministic model. It is observed that the corresponding stochastic model is stable in mean square when the intensity of noise is small.

APA, Harvard, Vancouver, ISO, and other styles

5

Reyes-Bahamón, Francisco J., Simeón Casanova Trujillo, and Eduardo González-Olivares. "Dynamics of a Leslie-Gower type predation model with non-monotonic functional response and weak Allee effect on prey." Selecciones Matemáticas 10, no. 02 (2023): 310–23. http://dx.doi.org/10.17268/sel.mat.2023.02.07.

Full text

Abstract:

This research concerns with analysis of a class of modified predator- prey type Leslie-Gower models. The model is described by an autonomous nonlinear ordinary differential equation system. The functional response of predators is Holling IV type or non-monotone, and the growth of prey is affected by the Allee effect. An important aspect is the study of the point (0, 0) since it has a strong influence on the behavior of the system being essential for the existence and extinction of both species, although the proposed system is not define there.

APA, Harvard, Vancouver, ISO, and other styles

6

Madhusudanan, V., and S. Vijaya. "Stability analysis in prey–predator system with mixed functional response." World Journal of Engineering 13, no. 4 (2016): 364–69. http://dx.doi.org/10.1108/wje-08-2016-048.

Full text

Abstract:

Purpose This paper aims to propose and analyse a two-prey–one-predator system with mixed functional response. Design/methodology/approach The predator exhibits Holling type IV functional response to one prey and Holling type I response to other. The occurrence of various positive equilibrium points with feasibility conditions are determined. The local and global stability of interior equilibrium points are examined. The boundedness of system is analysed. The sufficient conditions for persistence of the system is obtained by using Bendixson–Dulac criteria. Numerical simulations are carried out to illustrate the analytical findings. Findings The authors have derived the local and global stability condition of interior equilibrium of the system. Originality/value The authors observe that the critical values of some system parameter undergo Hopf bifurcation around some selective equilibrium. Hence, numerical simulations reveal the condition for the system to be stable and oscillatory.

APA, Harvard, Vancouver, ISO, and other styles

7

Gazi, Nurul Huda, and Subrata Kumar Biswas. "Holling-Tanner Predator-Prey Model with Type-IV Functional Response and Harvesting." Interdisciplinary journal of Discontinuity, Nonlinearity, and Complexity 10, no. 1 (2021): 151–59. http://dx.doi.org/10.5890/dnc.2021.03.011.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

Munde, Ashok. "Numerical Simulations of Prey-predator System with Holling Type-IV Functional Response." International Journal of Mathematics Trends and Technology 69, no. 4 (2023): 36–47. http://dx.doi.org/10.14445/22315373/ijmtt-v69i4p505.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

Yang, Deniu, Lihan Liu, and Hongyong Wang. "Traveling Wave Solution in a Diffusive Predator-Prey System with Holling Type-IV Functional Response." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/409264.

Full text

Abstract:

We establish the existence of traveling wave solution for a reaction-diffusion predator-prey system with Holling type-IV functional response. For simplicity, only one space dimension will be involved, the traveling solution equivalent to the heteroclinic orbits inR3. The methods used to prove the result are the shooting argument and the invariant manifold theory.

APA, Harvard, Vancouver, ISO, and other styles

10

Baek, Hunki. "A food chain system with Holling type IV functional response and impulsive perturbations." Computers & Mathematics with Applications 60, no. 5 (2010): 1152–63. http://dx.doi.org/10.1016/j.camwa.2010.05.039.

Full text

APA, Harvard, Vancouver, ISO, and other styles

11

Ramadhani, Nur Suci, Toaha Toaha, and Kasbawati Kasbawati. "Dynamics Analysis of Modified Leslie-Gower Model with Simplified Holling Type IV Functional Response." Jurnal Matematika, Statistika dan Komputasi 18, no. 1 (2021): 12–21. http://dx.doi.org/10.20956/j.v18i1.13881.

Full text

Abstract:

In this paper, the modified Leslie-Gower predator-prey model with simplified Holling type IV functional response is discussed. It is assumed that the prey population is a dangerous population. The equilibrium point of the model and the stability of the coexistence equilibrium point are analyzed. The simulation results show that both prey and predator populations will not become extinct as time increases. When the prey population density increases, there is a decrease in the predatory population density because the dangerous prey population has a better ability to defend itself from predators when the number is large enough.

APA, Harvard, Vancouver, ISO, and other styles

12

Zhang, Jun, and Juan Su. "Bifurcations in a Predator–Prey Model of Leslie-Type with Simplified Holling Type IV Functional Response." International Journal of Bifurcation and Chaos 31, no. 04 (2021): 2150054. http://dx.doi.org/10.1142/s0218127421500541.

Full text

Abstract:

In this paper, we complete the remaining investigation of local bifurcations in a predator–prey model of Leslie-type with simplified Holling type IV functional response. The system has at most three equilibria, and local bifurcations were completely investigated in the cases of one and three equilibria, but in the case of two equilibria the previous study was only on a fixed parameter. We extend the study in the case of two equilibria for all parameters, and find that the system exhibits Hopf bifurcations of codimensions 1 and 2, and Bogdanov–Takens bifurcations of codimensions 2 and 3. Previous results and our research show that the codimension of local bifurcations is at most 3, and both focus type and cusp type Bogdanov–Takens bifurcations of codimension 3 can occur.

APA, Harvard, Vancouver, ISO, and other styles

13

Upadhyay, Ranjit Kumar, and Sharada Nandan Raw. "Complex dynamics of a three species food-chain model with Holling type IV functional response." Nonlinear Analysis: Modelling and Control 16, no. 3 (2011): 553–374. http://dx.doi.org/10.15388/na.16.3.14098.

Full text

Abstract:

In this paper, dynamical complexities of a three species food chain model with Holling type IV predator response is investigated analytically as well as numerically. The local and global stability analysis is carried out. The persistence criterion of the food chain model is obtained. Numerical bifurcation analysis reveals the chaotic behavior in a narrow region of the bifurcation parameter space for biologically realistic parameter values of the model system. Transition to chaotic behavior is established via period-doubling bifurcation and some sequences of distinctive period-halving bifurcation leading to limit cycles are observed.

APA, Harvard, Vancouver, ISO, and other styles

14

Wang, Yanzhen, and Min Zhao. "Dynamic Analysis of an Impulsively Controlled Predator-Prey Model with Holling Type IV Functional Response." Discrete Dynamics in Nature and Society 2012 (2012): 1–18. http://dx.doi.org/10.1155/2012/141272.

Full text

Abstract:

The dynamic behavior of a predator-prey model with Holling type IV functional response is investigated with respect to impulsive control strategies. The model is analyzed to obtain the conditions under which the system is locally asymptotically stable and permanent. Existence of a positive periodic solution of the system and the boundedness of the system is also confirmed. Furthermore, numerical analysis is used to discover the influence of impulsive perturbations. The system is found to exhibit rich dynamics such as symmetry-breaking pitchfork bifurcation, chaos, and nonunique dynamics.

APA, Harvard, Vancouver, ISO, and other styles

15

Liu, Xinxin, and Qingdao Huang. "The dynamics of a harvested predator–prey system with Holling type IV functional response." Biosystems 169-170 (July 2018): 26–39. http://dx.doi.org/10.1016/j.biosystems.2018.05.005.

Full text

APA, Harvard, Vancouver, ISO, and other styles

16

Shalan, Rehab Noori, Dina Aljaf, and Hiba Abdullah Ibrahim. "Global Stability of Harmful Phytoplankton and Herbivorous Zooplankton with Holling Type IV Functional Response." Journal of Al-Nahrain University-Science 19, no. 2 (2016): 117–23. http://dx.doi.org/10.22401/jnus.19.2.15.

Full text

APA, Harvard, Vancouver, ISO, and other styles

17

Huang, Meihua, and Xuepeng Li. "Dispersal permanence of a periodic predator–prey system with Holling type-IV functional response." Applied Mathematics and Computation 218, no. 2 (2011): 502–13. http://dx.doi.org/10.1016/j.amc.2011.05.092.

Full text

APA, Harvard, Vancouver, ISO, and other styles

18

Fu, Jing, Daqing Jiang, Ningzhong Shi, Tasawar Hayat, and Baslur Abmad. "Dynamical behavior of a stochastic ratio-dependent predator-prey system with Holling type IV functional response." Filomat 32, no. 19 (2018): 6549–62. http://dx.doi.org/10.2298/fil1819549f.

Full text

Abstract:

In this paper, we investigate the dynamical properties of a stochastic ratio-dependent predatorprey system with Holling type IV functional response. The existence of the globally positive solutions to the system with positive initial value is shown employing comparison theorem of stochastic equation and It??s formula. We derived some sufficient conditions for the persistence in mean and extinction. This system has a stable stationary distribution which is ergodic. Numerical simulations are carried out for further support of present research.

APA, Harvard, Vancouver, ISO, and other styles

19

Siddik, A. Muh Amil, Syamsuddin Toaha, and Andi Muhammad Anwar. "Stability Analysis of Prey-Predator Model With Holling Type IV Functional Response and Infectious Predator." Jurnal Matematika, Statistika dan Komputasi 17, no. 2 (2020): 155–65. http://dx.doi.org/10.20956/jmsk.v17i2.11716.

Full text

Abstract:

Stability of equilibrium points of the prey-predator model with diseases that spreads in predators where the predation function follows the simplified Holling type IV functional response are investigated. To find out the local stability of the equilibrium point of the model, the system is then linearized around the equilibrium point using the Jacobian matrix method, and stability of the equilibrium point is determined via the eigenvalues method. There exists three non-negative equilibrium points, except , that may exist and stable. Simulation results show that with the variation of several parameter values infection rate of disease , the diseases in the system may become endemic, or may become free from endemic.

APA, Harvard, Vancouver, ISO, and other styles

20

Ren, Jingli, and Xueping Li. "Bifurcations in a Seasonally Forced Predator–Prey Model with Generalized Holling Type IV Functional Response." International Journal of Bifurcation and Chaos 26, no. 12 (2016): 1650203. http://dx.doi.org/10.1142/s0218127416502035.

Full text

Abstract:

A seasonally forced predator–prey system with generalized Holling type IV functional response is considered in this paper. The influence of seasonal forcing on the system is investigated via numerical bifurcation analysis. Bifurcation diagrams for periodic solutions of periods one and two, containing bifurcation curves of codimension one and bifurcation points of codimension two, are obtained by means of a continuation technique, corresponding to different bifurcation cases of the unforced system illustrated in five bifurcation diagrams. The seasonally forced model exhibits more complex dynamics than the unforced one, such as stable and unstable periodic solutions of various periods, stable and unstable quasiperiodic solutions, and chaotic motions through torus destruction or cascade of period doublings. Finally, some phase portraits and corresponding Poincaré map portraits are given to illustrate these different types of solutions.

APA, Harvard, Vancouver, ISO, and other styles

21

Yousef, A. M., S. Z. Rida, Y. Gh Gouda, and A. S. Zaki. "Dynamical Behaviors of a Fractional-Order Predator–Prey Model with Holling Type IV Functional Response and Its Discretization." International Journal of Nonlinear Sciences and Numerical Simulation 20, no. 2 (2019): 125–36. http://dx.doi.org/10.1515/ijnsns-2017-0152.

Full text

Abstract:

AbstractIn this paper, we investigate the dynamical behaviors of a fractional-order predator–prey with Holling type IV functional response and its discretized counterpart. First, we seek the local stability of equilibria for the fractional-order model. Also, the necessary and sufficient conditions of the stability of the discretized model are achieved. Bifurcation types (include transcritical, flip and Neimark–Sacker) and chaos are discussed in the discretized system. Finally, numerical simulations are executed to assure the validity of the obtained theoretical results.

APA, Harvard, Vancouver, ISO, and other styles

22

Mukherjee, Debasis. "Fear induced dynamics on Leslie-Gower predator-prey system with Holling-type IV functional response." Jambura Journal of Biomathematics (JJBM) 3, no. 2 (2022): 49–57. http://dx.doi.org/10.34312/jjbm.v3i2.14348.

Full text

Abstract:

This paper analyzes the effect of fear in a Leslie-Gower predator-prey system with Holling type IV functional response. Firstly, we show positivity and boundedness of the system. Then we discuss the structure of the positive equilibrium point, dynamical behavior of all the steady states and long term survival of all the populations in the system. It is shown that fear factor has an impact on the prey and predator equilibrium densities. We have shown the occurrence of transcritical bifurcation around the axial steady state. The presence of a Hopf bifurcation near the interior steady state has been developed by choosing the level of fear as a bifurcation parameter. Furthermore, we discuss the character of the limit cycle generated by Hopf bifurcation. A global stability criterion of the positive steady state point is derived. Numerically, we checked our analytical findings.

APA, Harvard, Vancouver, ISO, and other styles

23

Amirabad, H. Qolizadeh, O. RabieiMotlagh, and H. M. MohammadiNejad. "Permanency in predator–prey models of Leslie type with ratio-dependent simplified Holling type-IV functional response." Mathematics and Computers in Simulation 157 (March 2019): 63–76. http://dx.doi.org/10.1016/j.matcom.2018.09.023.

Full text

APA, Harvard, Vancouver, ISO, and other styles

24

Agarwal, Manju, and Rachana Pathak. "Harvesting and Hopf Bifurcation in a Prey-Predator Model with Holling Type IV Functional Response." International Journal of Mathematics and Soft Computing 2, no. 1 (2012): 99. http://dx.doi.org/10.26708/ijmsc.2012.1.2.12.

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

Wang, Qi, Binxiang Dai, and Yuming Chen. "Multiple periodic solutions of an impulsive predator–prey model with Holling-type IV functional response." Mathematical and Computer Modelling 49, no. 9-10 (2009): 1829–36. http://dx.doi.org/10.1016/j.mcm.2008.09.008.

Full text

APA, Harvard, Vancouver, ISO, and other styles

26

Huang, Ji-cai. "Bifurcations and Chaos in a Discrete Predator-prey System with Holling Type-IV Functional Response." Acta Mathematicae Applicatae Sinica, English Series 21, no. 1 (2005): 157–76. http://dx.doi.org/10.1007/s10255-005-0227-x.

Full text

APA, Harvard, Vancouver, ISO, and other styles

27

Liu, Xinxin, and Qingdao Huang. "Analysis of optimal harvesting of a predator-prey model with Holling type IV functional response." Ecological Complexity 42 (March 2020): 100816. http://dx.doi.org/10.1016/j.ecocom.2020.100816.

Full text

APA, Harvard, Vancouver, ISO, and other styles

28

Shen, Chunxia. "Permanence and global attractivity of the food-chain system with Holling IV type functional response." Applied Mathematics and Computation 194, no. 1 (2007): 179–85. http://dx.doi.org/10.1016/j.amc.2007.04.019.

Full text

APA, Harvard, Vancouver, ISO, and other styles

29

Bhattacharyya, Rakhi, Banibrata Mukhopadhyay, and Malay Bandyopadhyay. "Diffusion-Driven Stability Analysis of A Prey-Predator System with Holling Type-IV Functional Response." Systems Analysis Modelling Simulation 43, no. 8 (2003): 1085–93. http://dx.doi.org/10.1080/0232929031000150409.

Full text

APA, Harvard, Vancouver, ISO, and other styles

30

Blé, Gamaliel, Víctor Castellanos, and Miguel A. Dela-Rosa. "Coexistence of species in a tritrophic food chain model with Holling functional response type IV." Mathematical Methods in the Applied Sciences 41, no. 16 (2018): 6683–701. http://dx.doi.org/10.1002/mma.5184.

Full text

APA, Harvard, Vancouver, ISO, and other styles

31

Lv, Luyao, and Xianyi Li. "Stability and Bifurcation Analysis in a Discrete Predator–Prey System of Leslie Type with Radio-Dependent Simplified Holling Type IV Functional Response." Mathematics 12, no. 12 (2024): 1803. http://dx.doi.org/10.3390/math12121803.

Full text

Abstract:

In this paper, we use a semi-discretization method to consider the predator–prey model of Leslie type with ratio-dependent simplified Holling type IV functional response. First, we discuss the existence and stability of the positive fixed point in total parameter space. Subsequently, through using the central manifold theorem and bifurcation theory, we obtain sufficient conditions for the flip bifurcation and Neimark–Sacker bifurcation of this system to occur. Finally, the numerical simulations illustrate the existence of Neimark–Sacker bifurcation and obtain some new dynamical phenomena of the system—the existence of a limit cycle. Corresponding biological meanings are also formulated.

APA, Harvard, Vancouver, ISO, and other styles

32

Rana, S. M. Sohel, and Umme Kulsum. "Bifurcation Analysis and Chaos Control in a Discrete-Time Predator-Prey System of Leslie Type with Simplified Holling Type IV Functional Response." Discrete Dynamics in Nature and Society 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/9705985.

Full text

Abstract:

The dynamic behavior of a discrete-time predator-prey system of Leslie type with simplified Holling type IV functional response is examined. We algebraically show that the system undergoes a bifurcation (flip or Neimark-Sacker) in the interior of R+2. Numerical simulations are presented not only to validate analytical results but also to show chaotic behaviors which include bifurcations, phase portraits, period 2, 4, 6, 8, 10, and 20 orbits, invariant closed cycle, and attracting chaotic sets. Furthermore, we compute numerically maximum Lyapunov exponents and fractal dimension to justify the chaotic behaviors of the system. Finally, a strategy of feedback control is applied to stabilize chaos existing in the system.

APA, Harvard, Vancouver, ISO, and other styles

33

Arsie, Alessandro, Chanaka Kottegoda, and Chunhua Shan. "A predator-prey system with generalized Holling type IV functional response and Allee effects in prey." Journal of Differential Equations 309 (February 2022): 704–40. http://dx.doi.org/10.1016/j.jde.2021.11.041.

Full text

APA, Harvard, Vancouver, ISO, and other styles

34

Lajmiri, Z., and R. Khoshsiar Ghaziani. "Hopf bifurcation and stability analysis of an predator-prey system with Holling type IV functional response." Journal of Applied Nonlinear Dynamics 7, no. 4 (2018): 337–48. http://dx.doi.org/10.5890/jand.2018.12.002.

Full text

APA, Harvard, Vancouver, ISO, and other styles

35

Huang1, Ji-cai, and Dong-mei Xiao2. "Analyses of Bifurcations and Stability in a Predator-prey System with Holling Type-IV Functional Response." Acta Mathematicae Applicatae Sinica, English Series 20, no. 1 (2004): 167–78. http://dx.doi.org/10.1007/s10255-004-0159-x.

Full text

APA, Harvard, Vancouver, ISO, and other styles

36

Yeh, Tzung-Shin. "Classification of bifurcation diagrams for a multiparameter diffusive logistic problem with Holling type-IV functional response." Journal of Mathematical Analysis and Applications 418, no. 1 (2014): 283–304. http://dx.doi.org/10.1016/j.jmaa.2014.03.067.

Full text

APA, Harvard, Vancouver, ISO, and other styles

37

Ciou, Jyun-Yuan, and Tzung-Shin Tzung-Shin. "Complete classification of bifurcation curves for a multiparameter diffusive logistic problem with generalized Holling type-IV functional response." Electronic Journal of Differential Equations 2021, no. 01-104 (2021): 10. http://dx.doi.org/10.58997/ejde.2021.10.

Full text

Abstract:

We study exact multiplicity and bifurcation curves of positive solutions for the diffusive logistic problem with generalized Holling type-IV functional response $$\displaylines{ u''(x)+\lambda \big[ ru(1-\frac{u}{q})-\frac{u}{1+mu+u^2}\big] =0,\quad-1<x<1, \cr u(-1)=u(1)=0, }$$ where the quantity in brackets is the growth rate function and \(\lambda >0\) is a bifurcation parameter. On the \((\lambda ,||u||_{\infty })\)-plane, we give a complete classification of two qualitatively different bifurcation curves: a C-shaped curve and a monotone increasing curve. For more information see https://ejde.math.txstate.edu/Volumes/2021/10/abstr.html

APA, Harvard, Vancouver, ISO, and other styles

38

Huang, Jicai, Xiaojing Xia, Xinan Zhang, and Shigui Ruan. "Bifurcation of Codimension 3 in a Predator–Prey System of Leslie Type with Simplified Holling Type IV Functional Response." International Journal of Bifurcation and Chaos 26, no. 02 (2016): 1650034. http://dx.doi.org/10.1142/s0218127416500346.

Full text

Abstract:

It was shown in [Li & Xiao, 2007] that in a predator–prey model of Leslie type with simplified Holling type IV functional response some complex bifurcations can occur simultaneously for some values of parameters, such as codimension 1 subcritical Hopf bifurcation and codimension 2 Bogdanov–Takens bifurcation. In this paper, we show that for the same model there exists a unique degenerate positive equilibrium which is a degenerate Bogdanov–Takens singularity (focus case) of codimension 3 for other values of parameters. We prove that the model exhibits degenerate focus type Bogdanov–Takens bifurcation of codimension 3 around the unique degenerate positive equilibrium. Numerical simulations, including the coexistence of three hyperbolic positive equilibria, two limit cycles, bistability states (one stable equilibrium and one stable limit cycle, or two stable equilibria), tristability states (two stable equilibria and one stable limit cycle), a stable limit cycle enclosing a homoclinic loop, a homoclinic loop enclosing an unstable limit cycle, or a stable limit cycle enclosing three unstable hyperbolic positive equilibria for various parameter values, confirm the theoretical results.

APA, Harvard, Vancouver, ISO, and other styles

39

Lian, Fuyun, and Yuantong Xu. "Hopf bifurcation analysis of a predator–prey system with Holling type IV functional response and time delay." Applied Mathematics and Computation 215, no. 4 (2009): 1484–95. http://dx.doi.org/10.1016/j.amc.2009.07.003.

Full text

APA, Harvard, Vancouver, ISO, and other styles

40

Liu, Yun, and Xijuan Liu. "Mode Locking, Farey Sequence, and Bifurcation in a Discrete Predator-Prey Model with Holling Type IV Response." Axioms 14, no. 6 (2025): 414. https://doi.org/10.3390/axioms14060414.

Full text

Abstract:

This paper presents and examines a discrete-time predator–prey model of the Leslie type, integrating a Holling type IV functional response for analysis. The mathematical analysis succinctly identifies fixed points and evaluates their local stability within the model. The study employs the normal form approach and bifurcation theory to explore codimension-one and two bifurcation behaviors for this model. The primary conclusions are substantiated by a combination of rigorous theoretical analysis and meticulous computational simulations. Additionally, utilizing fractal basin boundaries, periodicity variations, and Lyapunov exponent distributions within two-parameter spaces, we observe a mode-locking structure akin to Arnold tongues. These periods are arranged in a Farey tree sequence and embedded within quasi-periodic/chaotic regions. These findings enhance comprehension of bifurcation cascade emergence and structural patterns in diverse biological systems with discrete dynamics.

APA, Harvard, Vancouver, ISO, and other styles

41

Dai, Yanfei, and Yulin Zhao. "Hopf Cyclicity and Global Dynamics for a Predator–Prey System of Leslie Type with Simplified Holling Type IV Functional Response." International Journal of Bifurcation and Chaos 28, no. 13 (2018): 1850166. http://dx.doi.org/10.1142/s0218127418501663.

Full text

Abstract:

This paper is concerned with a predator–prey model of Leslie type with simplified Holling type IV functional response, provided that it has either a unique nondegenerate positive equilibrium or three distinct positive equilibria. The type and stability of each equilibrium, Hopf cyclicity of each weak focus, and the number and distribution of limit cycles in the first quadrant are studied. It is shown that every equilibrium is not a center. If the system has a unique positive equilibrium which is a weak focus, then its order is at most [Formula: see text] and it has Hopf cyclicity [Formula: see text]. Moreover, some explicit conditions for the global stability of the unique equilibrium are established by applying Dulac’s criterion and constructing the Lyapunov function. If the system has three distinct positive equilibria, then one of them is a saddle and the others are both anti-saddles. For two anti-saddles, we prove that the Hopf cyclicity for the anti-saddle with smaller abscissa (resp., bigger abscissa) is [Formula: see text] (resp., [Formula: see text]). Furthermore, if both anti-saddle positive equilibria are weak foci, then they are unstable weak foci of order one. Moreover, one limit cycle can bifurcate from each of them simultaneously. Numerical simulations show that there is also a big stable limit cycle enclosing these two small limit cycles.

APA, Harvard, Vancouver, ISO, and other styles

42

马, 雅妮. "Hopf Bifurcation of a Modified Leslie-Gower Predator-Prey System with StrongAllee Effect and Holling Type-IV Functional Response." Advances in Applied Mathematics 13, no. 02 (2024): 539–53. http://dx.doi.org/10.12677/aam.2024.132053.

Full text

APA, Harvard, Vancouver, ISO, and other styles

43

GHOSH, UTTAM, PRAHLAD MAJUMDAR, and JAYANTA KUMAR GHOSH. "BIFURCATION ANALYSIS OF A TWO-DIMENSIONAL PREDATOR–PREY MODEL WITH HOLLING TYPE IV FUNCTIONAL RESPONSE AND NONLINEAR PREDATOR HARVESTING." Journal of Biological Systems 28, no. 04 (2020): 839–64. http://dx.doi.org/10.1142/s0218339020500199.

Full text

Abstract:

The aim of this paper is to investigate the dynamical behavior of a two-species predator–prey model with Holling type IV functional response and nonlinear predator harvesting. The positivity and boundedness of the solutions of the model have been established. The considered system contains three kinds of equilibrium points. Those are the trivial equilibrium point, axial equilibrium point and the interior equilibrium points. The trivial equilibrium point is always saddle and stability of the axial equilibrium point depends on critical value of the conversion efficiency. The interior equilibrium point changes its stability through various parametric conditions. The considered system experiences different types of bifurcations such as Saddle-node bifurcation, Hopf bifurcation, Transcritical bifurcation and Bogdanov–Taken bifurcation. It is clear from the numerical analysis that the predator harvesting rate and the conversion efficiency play an important role in stability of the system.

APA, Harvard, Vancouver, ISO, and other styles

44

Shang, Zuchong, Yuanhua Qiao, Lijuan Duan, and Jun Miao. "Stability and Bifurcation Analysis in a Nonlinear Harvested Predator–Prey Model with Simplified Holling Type IV Functional Response." International Journal of Bifurcation and Chaos 30, no. 14 (2020): 2050205. http://dx.doi.org/10.1142/s0218127420502053.

Full text

Abstract:

In this paper, a type of predator–prey model with simplified Holling type IV functional response is improved by adding the nonlinear Michaelis–Menten type prey harvesting to explore the dynamics of the predator–prey system. Firstly, the conditions for the existence of different equilibria are analyzed, and the stability of possible equilibria is investigated to predict the final state of the system. Secondly, bifurcation behaviors of this system are explored, and it is found that saddle-node and transcritical bifurcations occur on the condition of some parameter values using Sotomayor’s theorem; the first Lyapunov constant is computed to determine the stability of the bifurcated limit cycle of Hopf bifurcation; repelling and attracting Bogdanov–Takens bifurcation of codimension 2 is explored by calculating the universal unfolding near the cusp based on two-parameter bifurcation analysis theorem, and hence there are different parameter values for which the model has a limit cycle, or a homoclinic loop; it is also predicted that the heteroclinic bifurcation may occur as the parameter values vary by analyzing the isoclinic of the improved system. Finally, numerical simulations are done to verify the theoretical analysis.

APA, Harvard, Vancouver, ISO, and other styles

45

Parshad, Rana D., Ranjit Kumar Upadhyay, Swati Mishra, Satish Kumar Tiwari, and Swarnali Sharma. "On the explosive instability in a three-species food chain model with modified Holling type IV functional response." Mathematical Methods in the Applied Sciences 40, no. 16 (2017): 5707–26. http://dx.doi.org/10.1002/mma.4419.

Full text

APA, Harvard, Vancouver, ISO, and other styles

46

Wang, Baiming, and Xianyi Li. "Modeling and Dynamical Analysis of a Fractional-Order Predator–Prey System with Anti-Predator Behavior and a Holling Type IV Functional Response." Fractal and Fractional 7, no. 10 (2023): 722. http://dx.doi.org/10.3390/fractalfract7100722.

Full text

Abstract:

We here investigate the dynamic behavior of continuous and discrete versions of a fractional-order predator–prey system with anti-predator behavior and a Holling type IV functional response. First, we establish the non-negativity, existence, uniqueness and boundedness of solutions to the system from a mathematical analysis perspective. Then, we analyze the stability of its equilibrium points and the possibility of bifurcations using stability analysis methods and bifurcation theory, demonstrating that, under specific parameter conditions, the continuous system exhibits a Hopf bifurcation, while the discrete version exhibits a Neimark–Sacker bifurcation and a period-doubling bifurcation. After providing numerical simulations to illustrate the theoretically derived conclusions and by summarizing the various analytical results obtained, we finally present four interesting conclusions that can contribute to better management and preservation of ecological systems.

APA, Harvard, Vancouver, ISO, and other styles

47

Zhang, Rui-Ling. "Optimal Harvesting Policy of Discrete-Time Predator-Prey Dynamic System with Holling Type-IV Functional Response and Its Simulation." Applied and Computational Mathematics 4, no. 1 (2015): 20. http://dx.doi.org/10.11648/j.acm.20150401.14.

Full text

APA, Harvard, Vancouver, ISO, and other styles

48

Chai, Chuanfu, Yuanfu Shao, and Yaping Wang. "Analysis of a Holling-type IV stochastic prey-predator system with anti-predatory behavior and Lévy noise." AIMS Mathematics 8, no. 9 (2023): 21033–54. http://dx.doi.org/10.3934/math.20231071.

Full text

Abstract:

<abstract><p>In this paper, we investigate a stochastic prey-predator model with Holling-type IV functional responses, anti-predatory behavior (referring to prey resistance to predator), gestation time delay of prey and Lévy noise. We investigate the existence and uniqueness of global positive solutions through Itô's formulation and Lyapunov's method. We also provide sufficient conditions for the persistence and extinction of prey-predator populations. Additionally, we examine the stability of the system distribution and validate our analytical findings through detailed numerical simulations. Our paper concludes with the implications of our results.</p></abstract>

APA, Harvard, Vancouver, ISO, and other styles

49

Rajinder, Pal Kaur. "Impact of Fear Effect on Plankton Dynamical System." Journal of Innovation Sciences and Sustainable Technologies 4, no. 1 (2024): 19–30. https://doi.org/10.0517/JISST.2024751635.

Full text

Abstract:

In this paper, we examine the effect of anti-predator behavior due to fear effect (K) on the 2-D plankton dynamical system involving phytoplankton and zooplankton species. We assume that phytoplankton species have developed defense mechanisms against zooplankton predation. The density of zooplankton decreased in the presence of anti-predator response of phytoplankton. It is determined that fear in phytoplankton can influence not only plankton demography but also terminate planktonic blooms. Our mathematical study reveals that low level fear can stabilize the system dynamics model involving Holling-type IV functional response. The boundedness of the solutions of the mathematical model is discussed. The equilibria and local stability of a given dynamical system are analyzed. Bifurcation is carried out considering (K) and (r) as bifurcation parameters. Numerical simulation is performed to support analytical results.

APA, Harvard, Vancouver, ISO, and other styles

50

Shang, Zuchong, and Yuanhua Qiao. "Bifurcation analysis of a Leslie-type predator–prey system with simplified Holling type IV functional response and strong Allee effect on prey." Nonlinear Analysis: Real World Applications 64 (April 2022): 103453. http://dx.doi.org/10.1016/j.nonrwa.2021.103453.

Full text

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!