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Journal articles on the topic 'Global equilibrium'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 February 2022

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1

Miao, Hui, Xamxinur Abdurahman, and Ahmadjan Muhammadhaji. "Global Stability of HIV-1 Infection Model with Two Time Delays." Abstract and Applied Analysis 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/163484.

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We investigate global dynamics for a system of delay differential equations which describes a virus-immune interaction in vivo. The model has two time delays describing time needed for infection of cell and CTLs generation. Our model admits three possible equilibria: infection-free equilibrium, CTL-absent infection equilibrium, and CTL-present infection equilibrium. The effect of time delay on stability of the equilibria of the CTL immune response model has been studied.

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2

Zhang, Yan, and Yan Chen. "TARIFF AND EQUILIBRIUM INDETERMINACY: A GLOBAL ANALYSIS." Macroeconomic Dynamics 16, S3 (2012): 394–410. http://dx.doi.org/10.1017/s1365100510000970.

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Zhang [Tariff and Equilibrium Indeterminacy, available at http://mpra.ub.uni-muenchen.de/13099/ (2009)] shows that endogenous tariffs (or energy taxes) and endogenous labor income taxes are equivalent in generating local indeterminacy. Using methods developed by Stockman [Journal of Economic Theory 145 (2010), 1060–1085], we extend Zhang's analysis to prove that endogenous tariffs and endogenous labor income taxes are also equivalent in generating global indeterminacy (chaotic equilibria) under a balanced-budget rule. More precisely, we show that the existence of Euler equation branching in an

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3

Ara, Tomohiro. "Global Sourcing in Industry Equilibrium." Japanese Economic Review 65, no. 1 (2013): 93–115. http://dx.doi.org/10.1111/jere.12010.

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4

Carlsson, Hans, and Eric van Damme. "Global Games and Equilibrium Selection." Econometrica 61, no. 5 (1993): 989. http://dx.doi.org/10.2307/2951491.

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5

Khan, Muhammad Altaf, Yasir Khan, Sehra Khan, and Saeed Islam. "Global stability and vaccination of an SEIVR epidemic model with saturated incidence rate." International Journal of Biomathematics 09, no. 05 (2016): 1650068. http://dx.doi.org/10.1142/s1793524516500686.

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This study considers SEIVR epidemic model with generalized nonlinear saturated incidence rate in the host population horizontally to estimate local and global equilibriums. By using the Routh–Hurwitz criteria, it is shown that if the basic reproduction number [Formula: see text], the disease-free equilibrium is locally asymptotically stable. When the basic reproduction number exceeds the unity, then the endemic equilibrium exists and is stable locally asymptotically. The system is globally asymptotically stable about the disease-free equilibrium if [Formula: see text]. The geometric approach i

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6

WANG, SHIFEI, and DINGYU ZOU. "VIRAL DYNAMICS IN A DISTRIBUTED TIME DELAYED HCV PATHOGENESIS MODEL." International Journal of Biomathematics 05, no. 06 (2012): 1250056. http://dx.doi.org/10.1142/s1793524512500568.

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In this paper, we investigate global dynamics for a distributed time delayed HCV infection model. Our model admits two possible equilibria, an uninfected equilibrium and infected equilibrium depending on the basic reproduction number. By employing the method of Lyapunov functional, we prove that the uninfected equilibrium is global asymptotically stable if the basic reproduction number is less than one, it is unstable and the infected equilibrium is global asymptotically stable if the basic reproduction number is larger than one. The simulations results are in good accordance with our analytic

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7

Ávila-Vales, Eric, Abraham Canul-Pech, and Erika Rivero-Esquivel. "Global stability of a distributed delayed viral model with general incidence rate." Open Mathematics 16, no. 1 (2018): 1374–89. http://dx.doi.org/10.1515/math-2018-0117.

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AbstractIn this paper, we discussed a infinitely distributed delayed viral infection model with nonlinear immune response and general incidence rate. We proved the existence and uniqueness of the equilibria. By using the Lyapunov functional and LaSalle invariance principle, we obtained the conditions of global stabilities of the infection-free equilibrium, the immune-exhausted equilibrium and the endemic equilibrium. Numerical simulations are given to verify the analytical results.

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8

OKUGUCHI, KOJI, and TAKESHI YAMAZAKI. "STABILITY OF EQUILIBRIUM IN BERTRAND AND COURNOT DUOPOLIES." International Game Theory Review 06, no. 03 (2004): 381–90. http://dx.doi.org/10.1142/s0219198904000265.

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We analyze the global stability of the equilibria in Bertrand and Cournot duopolies. Assuming a set of sufficient conditions for the global stability of the Bertrand duopoly equilibrium, we derive additional conditions which are sufficient for the global stability of the Cournot duopoly equilibrium. We use the relationships among the first and second order partial derivatives of the ordinary and inverse demand functions in deriving our results.

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9

Lu, Jinna, Xiaoguang Zhang, and Rui Xu. "Global stability and Hopf bifurcation of an eco-epidemiological model with time delay." International Journal of Biomathematics 12, no. 06 (2019): 1950062. http://dx.doi.org/10.1142/s1793524519500621.

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In this paper, an eco-epidemiological model with time delay representing the gestation period of the predator is investigated. In the model, it is assumed that the predator population suffers a transmissible disease and the infected predators may recover from the disease and become susceptible again. By analyzing corresponding characteristic equations, the local stability of each of feasible equilibria and the existence of Hopf bifurcations at the disease-free and coexistence equilibria are established, respectively. By means of Lyapunov functionals and LaSalle’s invariance principle, sufficie

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10

Qureshi, S. M., and A. Q. Khan. "Global Dynamics of a 3 × 6 System of Difference Equations." Discrete Dynamics in Nature and Society 2019 (July 1, 2019): 1–14. http://dx.doi.org/10.1155/2019/9797242.

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In the proposed work, global dynamics of a 3×6 system of rational difference equations has been studied in the interior of R+3. It is proved that system has at least one and at most seven boundary equilibria and a unique +ve equilibrium under certain parametric conditions. By utilizing method of Linearization, local dynamical properties about equilibria have been investigated. It is shown that every +ve solution of the system is bounded, and equilibrium P0 becomes a globally asymptotically stable if α1<α2,α4<α5, α7<α8. It is also shown that every +ve solution of the system converges t

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11

Yang, Yan Yan, Hui Wang, Zhi Xing Hu, and Wan Biao Ma. "Global Dynamics of a HIV Infection Model with Delayed CTL Response and Cure Rate." Advanced Materials Research 791-793 (September 2013): 1322–27. http://dx.doi.org/10.4028/www.scientific.net/amr.791-793.1322.

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In this paper, we have considered a viral infection model with delayed CTL response and cure rate. For this model, we have researched the stability of these three equilibriums depend on two threshold parameters and , that is, if , the infected-free equilibrium is locally asymptotically stable; if , the infected equilibrium without CTL response is globally asymptotically stable; and if , the infected equilibrium exists, at he same time, we have found that the time delay can lead to Hopf bifurcations and stable periodic solutions when the is unstable.

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12

Shilo, V. P. "The method of global equilibrium search." Cybernetics and Systems Analysis 35, no. 1 (1999): 68–74. http://dx.doi.org/10.1007/bf02667916.

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13

Kazmer, David Owen. "Manufacturing outsourcing, onshoring, and global equilibrium." Business Horizons 57, no. 4 (2014): 463–72. http://dx.doi.org/10.1016/j.bushor.2014.03.005.

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14

Wang, Lili, and Rui Xu. "Global Dynamics of a Predator-Prey Model with Stage Structure and Delayed Predator Response." Discrete Dynamics in Nature and Society 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/724325.

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A Holling type II predator-prey model with time delay and stage structure for the predator is investigated. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria of the system is discussed. The existence of Hopf bifurcations at the coexistence equilibrium is established. By means of the persistence theory on infinite dimensional systems, it is proven that the system is permanent if the coexistence equilibrium exists. By using Lyapunov functionals and LaSalle’s invariance principle, it is shown that the predator-extinction equilibrium is glo

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15

Bernoussi, Amine, Abdelilah Kaddar, and Said Asserda. "Global Stability of a Delayed SIRI Epidemic Model with Nonlinear Incidence." International Journal of Engineering Mathematics 2014 (December 7, 2014): 1–6. http://dx.doi.org/10.1155/2014/487589.

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In this paper we propose the global dynamics of an SIRI epidemic model with latency and a general nonlinear incidence function. The model is based on the susceptible-infective-recovered (SIR) compartmental structure with relapse (SIRI). Sufficient conditions for the global stability of equilibria (the disease-free equilibrium and the endemic equilibrium) are obtained by means of Lyapunov-LaSalle theorem. Also some numerical simulations are given to illustrate this result.

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16

Tian, Xiaohong, and Rui Xu. "Global dynamics of a predator-prey system with Holling type II functional response." Nonlinear Analysis: Modelling and Control 16, no. 2 (2011): 242–53. http://dx.doi.org/10.15388/na.16.2.14109.

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In this paper, a predator-prey system with Holling type II functional response and stage structure is investigated. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria of the system is studied. The existence of the orbitally asymptotically stable periodic solution is established. By using suitable Lyapunov functions and the LaSalle invariance principle, it is proven that the predator-extinction equilibrium is globally asymptotically stable when the coexistence equilibrium is not feasible, and sufficient conditions are derived for the glob

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17

Zhang, Xiao, Rui Xu, and Qintao Gan. "Global Stability for a Delayed Predator-Prey System with Stage Structure for the Predator." Discrete Dynamics in Nature and Society 2009 (2009): 1–24. http://dx.doi.org/10.1155/2009/285934.

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A delayed predator-prey system with stage structure for the predator is investigated. By analyzing the corresponding characteristic equations, the local stability of equilibria of the system is discussed. The existence of Hopf bifurcation at the positive equilibrium is established. By using an iteration technique and comparison argument, respectively, sufficient conditions are derived for the global stability of the positive equilibrium and two boundary equilibria of the system. Numerical simulations are carried out to illustrate the theoretical results.

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18

Khan, A. Q., and M. N. Qureshi. "Global Dynamics and Bifurcations Analysis of a Two-Dimensional Discrete-Time Lotka-Volterra Model." Complexity 2018 (2018): 1–18. http://dx.doi.org/10.1155/2018/7101505.

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In this paper, global dynamics and bifurcations of a two-dimensional discrete-time Lotka-Volterra model have been studied in the closed first quadrant R2. It is proved that the discrete model has three boundary equilibria and one unique positive equilibrium under certain parametric conditions. We have investigated the local stability of boundary equilibria O(0,0), A(α1-1)/α3,0, B0,(α4-1)/α6 and the unique positive equilibrium C((α1-1)α6-α2(α4-1))/(α3α6-α2α5),(α3(α4-1)+α5(1-α1))/(α3α6-α2α5), by the method of linearization. It is proved that the discrete model undergoes a period-doubling bifurca

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19

Margolin, Victor. "Global Expansion or Global Equilibrium? Design and the World Situation." Design Issues 12, no. 2 (1996): 22. http://dx.doi.org/10.2307/1511710.

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20

Putra, Roni Tri, Sukatik, Sri Nita, and Yandraini Yunida. "Kestabilan Global Endemik Model Epidemi SEIR." Jurnal Ilmiah Poli Rekayasa 9, no. 2 (2014): 52. http://dx.doi.org/10.30630/jipr.9.2.72.

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In this paper, it will be studied global stability endemic of equilibrium points of a SEIR model with infectious force in latent, infected and immune period. From the model it will be found investigated the existence and its stability of points its equilibrium. The global stability of equilibrium points is depending on the value of the basic reproduction number If there is a unique endemic equilibrium which is globally asymptotically stable.

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21

Lamba, Harbir, Pavel Krejčí, and Dmitrii Rachinskii. "The global stability of a class of history-dependent macroeconomic models." Mathematical Modelling of Natural Phenomena 15 (2020): 49. http://dx.doi.org/10.1051/mmnp/2019061.

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We consider piecewise-linear, discrete-time, macroeconomic models that have a continuum of feasible equilibrium states. The non-trivial equilibrium set and resulting path-dependence are induced by stickiness in either expectations or the response of the Central Bank. For a low-dimensional variant of the model with one representative agent, and also for a multi-agent model, we show that when exogenous noise is absent from the system the continuum of equilibrium states is the global attractor and each solution trajectory converges exponentially to one of the equilibria. Further, when a uniformly

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22

WANG, SHIFEI, and YICANG ZHOU. "GLOBAL DYNAMICS OF AN IN-HOST HIV-1 INFECTION MODEL WITH THE LONG-LIVED INFECTED CELLS AND FOUR INTRACELLULAR DELAYS." International Journal of Biomathematics 05, no. 06 (2012): 1250058. http://dx.doi.org/10.1142/s1793524512500581.

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In this paper, we investigate global dynamics for an in-host HIV-1 infection model with the long-lived infected cells and four intracellular delays. Our model admits two possible equilibria, an uninfected equilibrium and infected equilibrium depending on the basic reproduction number. We derive that the global dynamics are completely determined by the values of the basic reproduction number: if the basic reproduction number is less than one, the uninfected equilibrium is globally asymptotically stable, and the virus is cleared; if the basic reproduction number is larger than one, then the infe

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23

Claussen, Martin, Victor Brovkin, Andrey Ganopolski, Claudia Kubatzki, and Vladimir Petoukhov. "Modelling global terrestrial vegetation–climate interaction." Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 353, no. 1365 (1998): 53–63. http://dx.doi.org/10.1098/rstb.1998.0190.

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By coupling an atmospheric general circulation model asynchronously with an equilibrium vegetation model, manifold equilibrium solutions of the atmosphere–biosphere system have been explored. It is found that under present–day conditions of the Earth's orbital parameters and sea–surface temperatures, two stable equilibria of vegetation patterns are possible: one corresponding to present–day sparse vegetation in the Sahel, the second solution yielding savannah which extends far into the south–western part of the Sahara. A similar picture is obtained for conditions during the last glacial maximu

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24

Maziane, Mehdi, Khalid Hattaf, and Noura Yousfi. "Spatiotemporal Dynamics of an HIV Infection Model with Delay in Immune Response Activation." International Journal of Differential Equations 2018 (2018): 1–9. http://dx.doi.org/10.1155/2018/3294268.

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We propose and analyse an human immunodeficiency virus (HIV) infection model with spatial diffusion and delay in the immune response activation. In the proposed model, the immune response is presented by the cytotoxic T lymphocytes (CTL) cells. We first prove that the model is well-posed by showing the global existence, positivity, and boundedness of solutions. The model has three equilibria, namely, the free-infection equilibrium, the immune-free infection equilibrium, and the chronic infection equilibrium. The global stability of the first two equilibria is fully characterized by two thresho

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25

Alkhudhari, Zainab, Sarah Al-Sheikh, and Salma Al-Tuwairqi. "Global Dynamics of a Mathematical Model on Smoking." ISRN Applied Mathematics 2014 (February 6, 2014): 1–7. http://dx.doi.org/10.1155/2014/847075.

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We derive and analyze a mathematical model of smoking in which the population is divided into four classes: potential smokers, smokers, temporary quitters, and permanent quitters. In this model we study the effect of smokers on temporary quitters. Two equilibria of the model are found: one of them is the smoking-free equilibrium and the other corresponds to the presence of smoking. We examine the local and global stability of both equilibria and we support our results by using numerical simulations.

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26

Bessey, K., M. Mavis, J. Rebaza, and J. Zhang. "Global Stability Analysis of a General Model of Zika Virus." Nonautonomous Dynamical Systems 6, no. 1 (2019): 18–34. http://dx.doi.org/10.1515/msds-2019-0002.

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AbstractMathematical models of Zika virus dynamics are relatively new, and they mostly focus on either vector and horizontal, or vector and vertical transmission only. In this work,we first revisit a recent model that considers vector and vertical transmission, and we provide an alternative proof on the global stability of the disease-free equilibrium point. Then, a new and general model is presented which includes vector, horizontal and vertical transmission. For this new model, existence of both a disease-free and an endemic equilibrium is studied. Using matrix and graph-theoretic methods, a

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27

Zhang, Xiaomin, Rui Xu, and Chenwei Song. "Stability and Hopf Bifurcation of a Delayed Viral Infection Dynamics Model with Immune Impairment." International Journal of Bifurcation and Chaos 31, no. 08 (2021): 2150141. http://dx.doi.org/10.1142/s0218127421501418.

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In this paper, we consider a viral infection dynamics model with immune impairment and time delay in immune expansion. By calculation, it is shown that the model has three equilibria: infection-free equilibrium, immunity-inactivated infection equilibrium, and immunity-activated infection equilibrium. By analyzing the distributions of roots of corresponding characteristic equations, the local stability of the infection-free equilibrium and the immunity-inactivated infection equilibrium is established. Furthermore, we discuss the existence of Hopf bifurcation at the immunity-activated infection

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28

Zhang, Yong Po, Ming Juan Ma, Ping Zuo, and Xin Liang. "Analysis of a Eco-Epidemiological Model with Disease in the Predator." Applied Mechanics and Materials 536-537 (April 2014): 861–64. http://dx.doi.org/10.4028/www.scientific.net/amm.536-537.861.

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In this paper we formulated and analyzed a eco-epidemiological model with disease in the predator, analysis of the existing conditions of equilibrium point, the sufficient condition of the local asymptotical stability of the equilibrium was studied with the method of latent root, the global asymptotical stability of two of the boundary equilibriums and the local asymptotical stability of the positive equilibrium is proved by using the Lyapunov function.

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29

Cui, Qianqian, Qinghui Du, and Li Wang. "Global Dynamics of a Generalized SIRS Epidemic Model with Constant Immigration." Mathematical Problems in Engineering 2020 (November 20, 2020): 1–9. http://dx.doi.org/10.1155/2020/7845390.

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In this paper, we discuss the global dynamics of a general susceptible-infected-recovered-susceptible (SIRS) epidemic model. By using LaSalle’s invariance principle and Lyapunov direct method, the global stability of equilibria is completely established. If there is no input of infectious individuals, the dynamical behaviors completely depend on the basic reproduction number. If there exists input of infectious individuals, the unique equilibrium of model is endemic equilibrium and is globally asymptotically stable. Once one place has imported a disease case, then it may become outbreak after

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30

Hao, Ming Hong, and Wilma K. Olson. "The global equilibrium configurations of supercoiled DNA." Macromolecules 22, no. 8 (1989): 3292–303. http://dx.doi.org/10.1021/ma00198a017.

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31

Welsch, Heinz. "An Equilibrium Framework for Global Pollution Problems." Journal of Environmental Economics and Management 25, no. 1 (1993): S64—S79. http://dx.doi.org/10.1006/jeem.1993.1033.

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32

Yang, Haijun, and Jiang Zhu. "Equilibrium thermal response timescale of global oceans." Geophysical Research Letters 38, no. 14 (2011): n/a. http://dx.doi.org/10.1029/2011gl048076.

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33

Benhabib, J., M. Majumdar, and K. Nishimura. "Global equilibrium dynamics with stationary recursive preferences." Journal of Economic Behavior & Organization 8, no. 3 (1987): 429–52. http://dx.doi.org/10.1016/0167-2681(87)90054-0.

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34

Sandholm, William H. "Almost global convergence to p -dominant equilibrium." International Journal of Game Theory 30, no. 1 (2001): 107–16. http://dx.doi.org/10.1007/s001820100067.

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35

Tian, Xiaohong, and Rui Xu. "Global Stability of a Virus Infection Model with Time Delay and Absorption." Discrete Dynamics in Nature and Society 2011 (2011): 1–20. http://dx.doi.org/10.1155/2011/152415.

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In this paper, a virus infection model with time delay and absorption is studied. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria of the model is established. By using comparison arguments, it is shown that the infection free equilibrium is globally asymptotically stable when the basic reproduction ratio is less than unity. When the basic reproduction ratio is greater than unity, sufficient conditions are derived for the global stability of the virus-infected equilibrium. Numerical simulations are carried out to illustrate the theoret

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36

Li, Dan, Wanbiao Ma, and Songbai Guo. "Stability of a mathematical model of tumour-induced angiogenesis." Nonlinear Analysis: Modelling and Control 21, no. 3 (2016): 325–44. http://dx.doi.org/10.15388/na.2016.3.3.

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A model consisting of three differential equations to simulate the interactions between cancer cells, the angiogenic factors and endothelial progenitor cells in tumor growth is developed. Firstly, the global existence, nonnegativity and boundedness of the solutions are discussed. Secondly, by analyzing the corresponding characteristic equations, the local stability of three boundary equilibria and the angiogenesis equilibrium of the model is discussed, respectively. We further consider global asymptotic stability of the boundary equilibria and the angiogenesis equilibrium by using the well-kno

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37

Shebalin, John V. "Absolute equilibrium entropy." Journal of Plasma Physics 56, no. 3 (1996): 419–26. http://dx.doi.org/10.1017/s0022377800019383.

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The entropy associated with absolute equilibrium ensemble theories of ideal, homogeneous, fluid and magnetofluid turbulence is discussed, and the three-dimensional fluid case is examined in detail. A σ function is defined, whose minimum value with respect to global parameters is the entropy. A comparison is made between the use of global functions σ and phase functions H (associated with the development of various H theorems of ideal turbulence). It is shown that the two approaches are complementary, though conceptually different: H theorems show that an isolated system tends to equilibrium, w

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38

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.

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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

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Lotfi, El Mehdi, Mehdi Maziane, Khalid Hattaf, and Noura Yousfi. "Partial Differential Equations of an Epidemic Model with Spatial Diffusion." International Journal of Partial Differential Equations 2014 (February 10, 2014): 1–6. http://dx.doi.org/10.1155/2014/186437.

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The aim of this paper is to study the dynamics of a reaction-diffusion SIR epidemic model with specific nonlinear incidence rate. The global existence, positivity, and boundedness of solutions for a reaction-diffusion system with homogeneous Neumann boundary conditions are proved. The local stability of the disease-free equilibrium and endemic equilibrium is obtained via characteristic equations. By means of Lyapunov functional, the global stability of both equilibria is investigated. More precisely, our results show that the disease-free equilibrium is globally asymptotically stable if the ba

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40

Yang, Kun, Xiangdong Xie, and Fengde Chen. "Global Stability of a Discrete Mutualism Model." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/709124.

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A discrete mutualism model is studied in this paper. By using the linear approximation method, the local stability of the interior equilibrium of the system is investigated. By using the iterative method and the comparison principle of difference equations, sufficient conditions which ensure the global asymptotical stability of the interior equilibrium of the system are obtained. The conditions which ensure the local stability of the positive equilibrium is enough to ensure the global attractivity are proved.

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41

Benton, Michael J. "The history of the biosphere: Equilibrium and non-equilibrium models of global diversity." Trends in Ecology & Evolution 2, no. 6 (1987): 153–56. http://dx.doi.org/10.1016/0169-5347(87)90065-6.

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42

Dong, Qinglai, and Wanbiao Ma. "Qualitative analysis of a chemostat model with inhibitory exponential substrate uptake and a time delay." International Journal of Biomathematics 07, no. 04 (2014): 1450045. http://dx.doi.org/10.1142/s1793524514500454.

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In this paper, we consider a simple chemostat model with inhibitory exponential substrate uptake and a time delay. A detailed qualitative analysis about existence and boundedness of its solutions and the local asymptotic stability of its equilibria are carried out. Using Lyapunov–LaSalle invariance principle, we show that the washout equilibrium is global asymptotic stability for any time delay. Using the fluctuation lemma, the sufficient condition of the global asymptotic stability of the positive equilibrium [Formula: see text] is obtained. Numerical simulations are also performed to illustr

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43

Wang, Lingshu, and Guanghui Feng. "Stability and Bifurcation Analysis on an Ecoepidemiological Model with Stage Structure and Time Delay." Abstract and Applied Analysis 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/727818.

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An ecoepidemiological predator-prey model with stage structure for the predator and time delay due to the gestation of the predator is investigated. The effects of a prey refuge with disease in the prey population are concerned. By analyzing the corresponding characteristic equations, the local stability of each of the feasible equilibria of the model is discussed. Further, it is proved that the model undergoes a Hopf bifurcation at the positive equilibrium. By means of appropriate Lyapunov functions and LaSalle’s invariance principle, sufficient conditions are obtained for the global stabilit

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44

Aboudramane, Guiro, Dramane Ouedraogo, and Harouna Ouedraogo. "Global stability for a discrete SIR epidemic model with delay in the general incidence function." International Journal of Applied Mathematical Research 8, no. 2 (2019): 32. http://dx.doi.org/10.14419/ijamr.v8i2.29528.

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In this paper, we construct a backward difference scheme for a class of general SIR epidemic model with general incidence function f. We use the step size h > 0, for the discretization. The dynamical properties are investigated (positivity and the boundedness of solution). By constructing the Lyapunov function, under the conditions that function f satisfies some assumptions. The global stabilities of equilibria are obtained. If the basic reproduction number R0<1, the disease-free equilibrium is globally asymptotically stable. If R0>1, the endemic equilibrium is globally asymptotically

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45

Elaiw, Ahmed M., Safiya F. Alshehaiween, and Aatef D. Hobiny. "Global properties of virus dynamics with B-cell impairment." Open Mathematics 17, no. 1 (2019): 1435–49. http://dx.doi.org/10.1515/math-2019-0113.

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Abstract In this paper we construct a class of virus dynamics models with impairment of B-cell functions. Two forms of the incidence rate have been considered, saturated and general. The well-posedness of the models is justified. The models admit two equilibria which are determined by the basic reproduction number R0. The global stability of each equilibrium is proven by utilizing Lyapunov function and LaSalle’s invariance principle. The theoretical results are illustrated by numerical simulations.

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Shylo, Oleg V., Oleg A. Prokopyev, and Vladimir P. Shylo. "Solving weighted MAX-SAT via global equilibrium search." Operations Research Letters 36, no. 4 (2008): 434–38. http://dx.doi.org/10.1016/j.orl.2007.11.007.

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BAILEY, RALPH W., and ROSEMARY CLARKE. "Global macroeconomic sustainability: a dynamic general equilibrium approach." Environment and Development Economics 5, no. 1 (2000): 177–94. http://dx.doi.org/10.1017/s1355770x00000127.

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Previous empirical studies assessing sustainability have adopted the weak sustainability indicator (WSI) which measures changes in the stock of physical and natural capital. Whereas these studies have been retrospective, we use a dynamic general equilibrium model to investigate global and regional sustainability over the period 1985–2050, focusing on fossil fuel extraction. Our standard scenario predicts increasing WSI values suggesting global sustainability in all periods to 2050 as, despite a rising world oil price, the introduction of backstop fuels in 2010 provides an alternative source of

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Frankel, David M., Stephen Morris, and Ady Pauzner. "Equilibrium selection in global games with strategic complementarities." Journal of Economic Theory 108, no. 1 (2003): 1–44. http://dx.doi.org/10.1016/s0022-0531(02)00018-2.

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Danabasoglu, Gokhan, James C. McWilliams, and William G. Large. "Approach to Equilibrium in Accelerated Global Oceanic Models." Journal of Climate 9, no. 5 (1996): 1092–110. http://dx.doi.org/10.1175/1520-0442(1996)009<1092:ateiag>2.0.co;2.

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Kalbach, C. "Toward a global exciton model: the equilibrium component." Journal of Physics G: Nuclear and Particle Physics 25, no. 1 (1999): 75–94. http://dx.doi.org/10.1088/0954-3899/25/1/008.

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