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Статті в журналах з теми "Equilibrium stability"

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Автор: Grafiati

Опубліковано: 7 липня 2024

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1

Suherman, Sofita, Fatmawati Fatmawati, and Cicik Alfiniyah. "Analisis Kestabilan dan Kontrol Optimal Model Matematika Penyebaran Penyakit Ebola dengan Penanganan Medis." Contemporary Mathematics and Applications (ConMathA) 1, no. 1 (August 9, 2019): 19. http://dx.doi.org/10.20473/conmatha.v1i1.14772.

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Ebola disease is one of an infectious disease caused by a virus. Ebola disease can be transmitted through direct contact with Ebola’s patient, infected medical equipment, and contact with the deceased individual. The purpose of this paper is to analyze the stability of equilibriums and to apply the optimal control of treatment on the mathematical model of the spread of Ebola with medical treatment. Model without control has two equilibria, namely non-endemic equilibrium (E0) and endemic equilibrium (E1) The existence of endemic equilibrium and local stability depends on the basic reproduction number (R0). The non-endemic equilibrium is locally asymptotically stable if R0 < 1 and endemic equilibrium tend to asymptotically stable if R0 >1 . The problem of optimal control is then solved by Pontryagin’s Maximum Principle. From the numerical simulation result, it is found that the control is effective to minimize the number of the infected human population and the number of the infected human with medical treatment population compare without control.

2

CURRAN, P. F., and L. O. CHUA. "STABILITY OF EQUILIBRIA OF NEURAL NETWORKS." International Journal of Bifurcation and Chaos 09, no. 10 (October 1999): 1941–55. http://dx.doi.org/10.1142/s0218127499001413.

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Sufficient conditions for local and global asymptotic stability of equilibria of some general classes of neural networks are presented. In the event that the interconnection matrix is block diagonally stable it is shown that the equilibrium is globally asymptotically stable if the cells are dissipative at the equilibrium. For a special class of networks the conditions of dissipativity are reduced to more readily-tested conditions of passivity. Equilibria are shown to be asymptotically stable essentially if the cells are locally passive.

3

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.

4

Yang, Shengxu. "Regional Stability of Switching Control Circuit Systems with Multiple Equilibria." Journal of Physics: Conference Series 2355, no. 1 (October 1, 2022): 012027. http://dx.doi.org/10.1088/1742-6596/2355/1/012027.

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Abstract This paper investigates the stability of systems of multi-equilibrium switching circuits. For a first-order switching circuit system with two subsystems containing unique equilibria and different equilibria, we first establish a sufficient condition for the stability of the region of the multi-equilibrium first-order switching circuit system, and then complete the proof of its stability by means of a general solution of the system state. Secondly, for the second-order multi-equilibrium switching circuit system, the sufficient condition for the stability of the second-order multi-equilibrium switching circuit system is given, and the feasibility of the theorem is finally proved by drawing on existing research results and related sufficient conditions. The conclusions obtained show that the system of first- and second-order multiple equilibria switching circuits in the region is regionally stable after the corresponding switching paths.

5

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.

6

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 (June 26, 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 equilibrium. Sufficient conditions are obtained for the global asymptotic stability of each feasible equilibria of the model by using LaSalle’s invariance principle and iteration technique, respectively. Numerical simulations are carried out to illustrate the main theoretical results.

7

Erbaugh, James T., Christopher W. Callahan, Rebecca Finger-Higgins, Melissa DeSiervo, Douglas T. Bolger, Michael Cox, and Richard B. Howarth. "Sociotechnical stability and equilibrium." Current Opinion in Environmental Sustainability 49 (April 2021): 33–41. http://dx.doi.org/10.1016/j.cosust.2021.01.003.

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8

Gilboa, Itzhak, and Akihiko Matsui. "Social Stability and Equilibrium." Econometrica 59, no. 3 (May 1991): 859. http://dx.doi.org/10.2307/2938230.

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9

Kesner, J., A. N. Simakov, D. T. Garnier, P. J. Catto, R. J. Hastie, S. I. Krasheninnikov, M. E. Mauel, T. Sunn Pedersen, and J. J. Ramos. "Dipole equilibrium and stability." Nuclear Fusion 41, no. 3 (March 2001): 301–8. http://dx.doi.org/10.1088/0029-5515/41/3/307.

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10

Tabuchi, Takatoshi, and Dao-Zhi Zeng. "Stability of Spatial Equilibrium*." Journal of Regional Science 44, no. 4 (November 2004): 641–60. http://dx.doi.org/10.1111/j.0022-4146.2004.00352.x.

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11

Aliprantis, C. D., and I. Topolyan. "Continuity and equilibrium stability." Journal of Mathematical Analysis and Applications 405, no. 1 (September 2013): 104–10. http://dx.doi.org/10.1016/j.jmaa.2013.03.037.

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12

Lailatuz Arromadhani and Budi Priyo Prawoto. "Stability Analysis of Monkeypox Transmission Model by Administering Vaccine." Numerical: Jurnal Matematika dan Pendidikan Matematika 7, no. 1 (June 25, 2023): 195–210. http://dx.doi.org/10.25217/numerical.v7i1.3481.

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Monkeypox is an infectious disease that affects mammals, including humans and some primates. Monkeypox transmission can be prevented by administering vaccinations to the human population. This study aims to construct and analyze the monkeypox transmission model's stability with vaccination. There are six sub-populations: Vaccinated humans ( ), Susceptible humans ( ), Infected human , Recovered human , Susceptible animal , and Infected human . Several steps are literature study, formulating assumptions, constructing models, finding equilibrium points, searching for reproduction numbers by next-generation matrix, analyzing stability, and numerical simulations using Matlab R02023b. From the model, three equilibria are obtained: disease-free equilibrium points, first endemic equilibrium points, and second endemic equilibrium points. Disease-free equilibrium point will be asymptotically stable at the vaccination rates and the animal transmission rate of the animal at the rate of . The first endemic equilibrium point ) will be stable for and . The second endemic equilibrium point will be stable for and . Based on numerical simulation results, it is obtained that the higher the vaccination rate and the lower the transmission rate in animals, the faster the transmission of monkeypox infections.

13

OKUGUCHI, KOJI, and TAKESHI YAMAZAKI. "STABILITY OF EQUILIBRIUM IN BERTRAND AND COURNOT DUOPOLIES." International Game Theory Review 06, no. 03 (September 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.

14

Pérez-Chavela, Ernesto, and Juan Manuel Sánchez-Cerritos. "Euler-type Relative Equilibria and their Stability in Spaces of Constant Curvature." Canadian Journal of Mathematics 70, no. 2 (April 1, 2018): 426–50. http://dx.doi.org/10.4153/cjm-2017-002-7.

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AbstractWe consider three point positivemasses moving onS2andH2. An Eulerian-relative equilibrium is a relative equilibrium where the three masses are on the same geodesic. In this paper we analyze the spectral stability of these kind of orbits where the mass at the middle is arbitrary and the masses at the ends are equal and located at the same distance from the central mass. For the case of S2, we found a positive measure set in the set of parameters where the relative equilibria are spectrally stable, and we give a complete classiûcation of the spectral stability of these solutions, in the sense that, except on an algebraic curve in the space of parameters, we can determine if the corresponding relative equilibriumis spectrally stable or unstable. OnH2, in the elliptic case, we prove that generically all Eulerian-relative equilibria are unstable; in the particular degenerate case when the two equal masses are negligible, we get that the corresponding solutions are spectrally stable. For the hyperbolic case we consider the system where the mass in the middle is negligible; in this case the Eulerian-relative equilibria are unstable.

15

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 threshold parameters that are the basic reproduction number R0 and the CTL immune response reproduction number R1. The stability of the last equilibrium depends on R0 and R1 as well as time delay τ in the CTL activation. We prove that the chronic infection equilibrium is locally asymptotically stable when the time delay is sufficiently small, while it loses its stability and a Hopf bifurcation occurs when τ passes through a certain critical value.

16

Hu, Zhixing, Shanshan Yin, and Hui Wang. "Stability and Hopf Bifurcation of a Vector-Borne Disease Model with Saturated Infection Rate and Reinfection." Computational and Mathematical Methods in Medicine 2019 (June 9, 2019): 1–17. http://dx.doi.org/10.1155/2019/1352698.

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This paper established a delayed vector-borne disease model with saturated infection rate and cure rate. First of all, according to the basic reproductive number R0, we determined the disease-free equilibrium E0 and the endemic equilibrium E1. Through the analysis of the characteristic equation, we consider the stability of two equilibriums. Furthermore, the effect on the stability of the endemic equilibrium E1 by delay was studied, the existence of Hopf bifurcations of this system in E1 was analyzed, and the length of delay to preserve stability was estimated. The direction and stability of the Hopf bifurcation were also been determined. Finally, we performed some numerical simulation to illustrate our main results.

17

A. Sabarmathi, C. Pooja ,. "A Fractional Order Approach in the Eco-epidemiological Model of Sugarcane Grassy Shoot Disease Using Controls." Tuijin Jishu/Journal of Propulsion Technology 44, no. 4 (October 16, 2023): 5909–15. http://dx.doi.org/10.52783/tjjpt.v44.i4.2024.

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In this paper, an eco-epidemiological model for grassy shoot disease with controls is formed and analyzed using Fractional Differential Equations. The infection-free and endemic equilibriums of the model are obtained. Using the Next generation matrix approach, the basic reproduction number is calculated. The local stability of infection-free equilibrium for integer and fractional order is analyzed. The global stability of the equilibria is found using the Lyapunov function. The sensitive parameters which spread the grassy shoot disease are identified using sensitivity analysis.

18

Lv, Ying, Zhixing Hu, and Fucheng Liao. "The stability and Hopf bifurcation for an HIV model with saturated infection rate and double delays." International Journal of Biomathematics 11, no. 03 (April 2018): 1850040. http://dx.doi.org/10.1142/s1793524518500407.

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An HIV infection model with saturated infection rate and double delays is investigated. First, the existence of the infection-free equilibrium [Formula: see text], the immune-exhausted equilibrium [Formula: see text] and the infected equilibrium [Formula: see text] with immunity in different conditions is shown. By analyzing the characteristic equation, we study the locally asymptotical stability of the trivial equilibrium, and the existence of Hopf bifurcations when two delays are used as the bifurcation parameter. Furthermore, we apply the Nyquist criterion to estimate the length of delay for which stability continues to hold. Then with suitable Lyapunov function and LaSalle’s invariance principle, the global stability of the three equilibriums is obtained. Finally, numerical simulations are presented to illustrate the main mathematical results.

19

Khabouze, Mostafa, Khalid Hattaf, and Noura Yousfi. "Stability Analysis of an Improved HBV Model with CTL Immune Response." International Scholarly Research Notices 2014 (October 29, 2014): 1–8. http://dx.doi.org/10.1155/2014/407272.

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To better understand the dynamics of the hepatitis B virus (HBV) infection, we introduce an improved HBV model with standard incidence function, cytotoxic T lymphocytes (CTL) immune response, and take into account the effect of the export of precursor CTL cells from the thymus and the role of cytolytic and noncytolytic mechanisms. The local stability of the disease-free equilibrium and the chronic infection equilibrium is obtained via characteristic equations. Furthermore, the global stability of both equilibria is established by using two techniques, the direct Lyapunov method for the disease-free equilibrium and the geometrical approach for the chronic infection equilibrium.

20

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 (June 13, 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 is used to present the global stability of the endemic equilibrium. For [Formula: see text], the endemic equilibrium is stable globally asymptotically. Finally, the numerical results are presented to justify the mathematical results.

21

SCHLEY, D. "Bifurcation and stability of periodic solutions of differential equations with state-dependent delays." European Journal of Applied Mathematics 14, no. 1 (February 2003): 3–14. http://dx.doi.org/10.1017/s0956792502005053.

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We consider periodic solutions which bifurcate from equilibria in simple population models which incorporate a state-dependent time delay of the discrete kind. The delay is a function of the current size of the population. Solutions near equilibria are constructed using perturbation methods to determine the sub/supercriticality of the bifurcation and hence their stability. The stability of the bifurcating solutions depends on the qualitative form of the delay function. This is in contrast to the stability of an equilibrium, which is determined purely by the actual value of this function at the equilibrium.

22

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 (December 26, 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.

23

Arifovic, Jasmina, and James Bullard. "INTRODUCTION TO THE SPECIAL ISSUE: NEW APPROACHES TO LEARNING IN MACROECONOMIC MODELS." Macroeconomic Dynamics 5, no. 02 (April 2001): 143–47. http://dx.doi.org/10.1017/s1365100501019010.

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The research questions addressed by the literature on learning in macroeconomics can be classified into four categories: First, there are issues related to the convergence and stability under learning in models with unique rational expectations equilibria. Authors here are concerned mainly with the learnability of a rational expectations equilibrium, as a measure of that equilibrium's plausibility as an observed outcome in an actual economy. Second, there are issues related to convergence and stability under learning in models with multiple rational expectations equilibria. In this case, learnability serves as an equilibrium selection device, helping economists decide which equilibria are the more likely to be actually observed among the many that exist under rational expectations. A third set of issues involves the examination of transitional dynamics that accompanies the equilibrium selection process. Following some type of unexpected strcutural change or change in policy regime, for instance, economies necessarily must follow temporary transitional paths to a rational expectations equilibrium associated with the new reality. Learning is sometimes used to help model such transitional dynamics. Finally, there are issues related to the examination of learning dynamics that are intrinsically different, even asymptotically, from the dynamics of the rational expectations versions of the models. In these cases, the learning dynamics do not converge to the rational expectations fixed points, and (unexploitable) expectational errors persist indefinitely. Some authors have tried to make use of this possibility in order to build explanations of otherwise puzzling macroeconomic phenomena based on constantly changing expectations.

24

Li, Dan, Wanbiao Ma, and Songbai Guo. "Stability of a mathematical model of tumour-induced angiogenesis." Nonlinear Analysis: Modelling and Control 21, no. 3 (May 20, 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-known Liapunov–LaSalle invariance principal. Finally, some numerical simulations are given to support the theoretical results.

25

Jiang, Jiao, and Yongli Song. "Stability and Bifurcation Analysis of a Delayed Leslie-Gower Predator-Prey System with Nonmonotonic Functional Response." Abstract and Applied Analysis 2013 (2013): 1–19. http://dx.doi.org/10.1155/2013/152459.

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A delayed Leslie-Gower predator-prey model with nonmonotonic functional response is studied. The existence and local stability of the positive equilibrium of the system with or without delay are completely determined in the parameter plane. Using the method of upper and lower solutions and monotone iterative scheme, a sufficient condition independent of delay for the global stability of the positive equilibrium is obtained. Hopf bifurcations induced by the ratio of the intrinsic growth rates of the predator and prey and by delay, respectively, are found. Employing the normal form theory, the direction and stability of Hopf bifurcations can be explicitly determined by the parameters of the system. Some numerical simulations are given to support and extend our theoretical results. Two limit cycles enclosing an equilibrium, one limit cycle enclosing three equilibria and different types of heteroclinic orbits such as connecting two equilibria and connecting a limit cycle and an equilibrium are also found by using analytic and numerical methods.

26

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.

27

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 (August 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, sufficient conditions are obtained for the global stability of the coexistence equilibrium, the disease-free equilibrium and the predator-extinct equilibrium of the system, respectively.

28

Moghadas, S. M., and A. B. Gumel. "An epidemic model for the transmission dynamics of HIV and another pathogen." ANZIAM Journal 45, no. 2 (October 2003): 181–93. http://dx.doi.org/10.1017/s1446181100013250.

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AbstractA five-dimensional deterministic model is proposed for the dynamics between HIV and another pathogen within a given population. The model exhibits four equilibria: a disease-free equilibrium, an HIV-free equilibrium, a pathogen-free equilibrium and a co-existence equilibrium. The existence and stability of these equilibria are investigated. A competitive finite-difference method is constructed for the solution of the non-linear model. The model predicts the optimal therapy level needed to eradicate both diseases.

29

Yakubu, Aisha Aliyu, Farah Aini Abdullah, and Yazariah Mohd Yatim. "Mathematical Model of Pertussis and Pneumonia Co-Infection in Infants with Maternally Derived Immunity." Sains Malaysiana 51, no. 7 (July 31, 2022): 2197–209. http://dx.doi.org/10.17576/jsm-2022-5107-21.

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The transmission dynamics of a pertussis-pneumonia co-infection model is analyzed. The model takes into account temporary immunity of infected infants and includes a maternally derived immunity compartment. The basic reproduction number of the co-infected model is obtained using the next generation matrix, and stability analysis is carried out. The model exhibits four equilibria, namely, the pertussis-free equilibrium, the pneumonia-free equilibrium, the co-infection-free equilibrium and co-infection endemic equilibrium. Subsequently, the local stability of the co-infection-free equilibrium is analyzed and is shown to be locally asymptotically stable. Similarly, by constructing a suitable Lyapunov function, the co-infection endemic equilibrium is shown to be globally asymptotically stable. Numerical simulations are carried out to illustrate the validity of these results.

30

Sun, Caixia, Lele Li, and Jianwen Jia. "Hopf bifurcation of an HIV-1 virus model with two delays and logistic growth." Mathematical Modelling of Natural Phenomena 15 (2020): 16. http://dx.doi.org/10.1051/mmnp/2019038.

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The paper establish and investigate an HIV-1 virus model with logistic growth, which also has intracellular delay and humoral immunity delay. The local stability of feasible equilibria are established by analyzing the characteristic equations. The globally stability of infection-free equilibrium and immunity-inactivated equilibrium are studied using the Lyapunov functional and LaSalles invariance principle. Besides, we prove that Hopf bifurcation will occur when the humoral immune delay pass through the critical value. And the stability of the positive equilibrium and Hopf bifurcations are investigated by using the normal form theory and the center manifold theorem. Finally, we confirm the theoretical results by numerical simulations.

31

LIU, LUJU, and XINCHUN GAO. "QUALITATIVE STUDY FOR A MULTI-DRUG RESISTANT TB MODEL WITH EXOGENOUS REINFECTION AND RELAPSE." International Journal of Biomathematics 05, no. 04 (May 16, 2012): 1250031. http://dx.doi.org/10.1142/s1793524511001763.

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One tuberculosis transmission model is formulated by incorporating exogenous reinfection, relapse, and two treatment stages of infectious TB cases. The global stability of the unique disease-free equilibrium is obtained by applying the comparison principle if the effective reproduction number for the full model is less than unity. The existence and stability of the boundary equilibria are given by introducing the invasion reproduction numbers. Furthermore, the existence and local stability of the endemic equilibrium are addressed under some conditions.

32

Xu, Jinhu, Wenxiong Xu, and Yicang Zhou. "Analysis of a delayed epidemic model with non-monotonic incidence rate and vertical transmission." International Journal of Biomathematics 07, no. 04 (June 25, 2014): 1450041. http://dx.doi.org/10.1142/s1793524514500417.

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A delayed SEIR epidemic model with vertical transmission and non-monotonic incidence is formulated. The equilibria and the threshold of the model have been determined on the bases of the basic reproduction number. The local stability of disease-free equilibrium and endemic equilibrium is established by analyzing the corresponding characteristic equations. By comparison arguments, it is proved that, if R0 < 1, the disease-free equilibrium is globally asymptotically stable. Whereas, the disease-free equilibrium is unstable if R0 > 1. Moreover, we show that the disease is permanent if the basic reproduction number is greater than one. Furthermore, the sufficient conditions are obtained for the global asymptotic stability of the endemic equilibrium when R0 > 1.

33

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 globally asymptotically stable when the coexistence equilibrium is not feasible, and the sufficient conditions are obtained for the global stability of the coexistence equilibrium.

34

Mbabazi, Fulgensia Kamugisha, Joseph Y. T. Mugisha, and Mark Kimathi. "Hopf-Bifurcation Analysis of Pneumococcal Pneumonia with Time Delays." Abstract and Applied Analysis 2019 (February 3, 2019): 1–21. http://dx.doi.org/10.1155/2019/3757036.

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In this paper, a mathematical model of pneumococcal pneumonia with time delays is proposed. The stability theory of delay differential equations is used to analyze the model. The results show that the disease-free equilibrium is asymptotically stable if the control reproduction ratioR0is less than unity and unstable otherwise. The stability of equilibria with delays shows that the endemic equilibrium is locally stable without delays and stable if the delays are under conditions. The existence of Hopf-bifurcation is investigated and transversality conditions are proved. The model results suggest that, as the respective delays exceed some critical value past the endemic equilibrium, the system loses stability through the process of local birth or death of oscillations. Further, a decrease or an increase in the delays leads to asymptotic stability or instability of the endemic equilibrium, respectively. The analytical results are supported by numerical simulations.

35

Dambrine, Marc, and Michel Pierre. "About stability of equilibrium shapes." ESAIM: Mathematical Modelling and Numerical Analysis 34, no. 4 (July 2000): 811–34. http://dx.doi.org/10.1051/m2an:2000105.

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36

Jardin, S. C., M. G. Bell, J. L. Johnson, S. M. Kaye, C. Kessel, R. LaHaye, J. Manickam, et al. "V. Magnetohydrodynamic Equilibrium and Stability." Fusion Technology 21, no. 3P1 (May 1992): 1123–213. http://dx.doi.org/10.13182/fst92-a29895.

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37

Hender, T. C., B. A. Carreras, L. A. Charlton, L. Garcia, H. R. Hicks, J. A. Holmes, and V. E. Lynch. "Torsatron equilibrium and stability studies." Nuclear Fusion 25, no. 10 (October 1, 1985): 1463–73. http://dx.doi.org/10.1088/0029-5515/25/10/009.

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38

Klar, H. "Stability of equilibrium-top atoms." Zeitschrift f�r Physik D Atoms, Molecules and Clusters 6, no. 2 (June 1987): 107–11. http://dx.doi.org/10.1007/bf01384596.

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39

Logan, J. D., and A. K. Kapila. "Hydrodynamic stability of chemical equilibrium." International Journal of Engineering Science 27, no. 12 (January 1989): 1651–59. http://dx.doi.org/10.1016/0020-7225(89)90158-4.

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40

Swinkels, Jeroen M. "Evolutionary stability with equilibrium entrants." Journal of Economic Theory 57, no. 2 (August 1992): 306–32. http://dx.doi.org/10.1016/0022-0531(92)90038-j.

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41

Kerner, Wolfgang. "Equilibrium and stability of tokamaks." International Journal for Numerical Methods in Fluids 11, no. 6 (October 20, 1990): 791–809. http://dx.doi.org/10.1002/fld.1650110606.

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42

Lu, C. L., and N. C. Perkins. "Nonlinear Spatial Equilibria and Stability of Cables Under Uni-axial Torque and Thrust." Journal of Applied Mechanics 61, no. 4 (December 1, 1994): 879–86. http://dx.doi.org/10.1115/1.2901571.

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Low tension cables subject to torque may form complex three-dimensional (spatial) equilibria. The resulting nonlinear static deformations, which are dominated by cable flexure and torsion, may produce interior loops or kinks that can seriously degrade the performance of the cable. Using Kirchhoffrod assumptions, a theoretical model governing cable flexure and torsion is derived herein and used to analyze (1) globally large equilibrium states, and (2) local equilibrium stability. For the broad class of problems described by pure boundary loading, the equilibrium boundary value problem is integrable and admits closed-form elliptic integral solutions. Attention is focused on the example problem of a cable subject to uni-axial torque and thrust. Closed-form solutions are presented for the complex three-dimensional equilibrium states which, heretofore, were analyzed using purely numerical methods. Moreover, the stability of these equilibrium states is assessed and new and important stability conclusions are drawn.

43

Liu, Chao, and Qingling Zhang. "Dynamical Behavior and Stability Analysis in a Stage-Structured Prey Predator Model with Discrete Delay and Distributed Delay." Abstract and Applied Analysis 2014 (2014): 1–15. http://dx.doi.org/10.1155/2014/184174.

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We propose a prey predator model with stage structure for prey. A discrete delay and a distributed delay for predator described by an integral with a strong delay kernel are also considered. Existence of two feasible boundary equilibria and a unique interior equilibrium are analytically investigated. By analyzing associated characteristic equation, local stability analysis of boundary equilibrium and interior equilibrium is discussed, respectively. It reveals that interior equilibrium is locally stable when discrete delay is less than a critical value. According to Hopf bifurcation theorem for functional differential equations, it can be found that model undergoes Hopf bifurcation around the interior equilibrium when local stability switch occurs and corresponding stable limit cycle is observed. Furthermore, directions of Hopf bifurcation and stability of the bifurcating periodic solutions are studied based on normal form theory and center manifold theorem. Numerical simulations are carried out to show consistency with theoretical analysis.

44

Yan, Caijuan, and Jianwen Jia. "Hopf Bifurcation of a Delayed Epidemic Model with Information Variable and Limited Medical Resources." Abstract and Applied Analysis 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/109372.

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We consider SIR epidemic model in which population growth is subject to logistic growth in absence of disease. We get the condition for Hopf bifurcation of a delayed epidemic model with information variable and limited medical resources. By analyzing the corresponding characteristic equations, the local stability of an endemic equilibrium and a disease-free equilibrium is discussed. If the basic reproduction ratioℛ0<1, we discuss the global asymptotical stability of the disease-free equilibrium by constructing a Lyapunov functional. Ifℛ0>1, we obtain sufficient conditions under which the endemic equilibriumE*of system is locally asymptotically stable. And we also have discussed the stability and direction of Hopf bifurcations. Numerical simulations are carried out to explain the mathematical conclusions.

45

Wei, Fengying, and Qiuyue Fu. "Globally asymptotic stability of a predator–prey model with stage structure incorporating prey refuge." International Journal of Biomathematics 09, no. 04 (April 22, 2016): 1650058. http://dx.doi.org/10.1142/s1793524516500583.

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This paper focuses on the stabilities of the equilibria to a predator–prey model with stage structure incorporating prey refuge. By analyzing the characteristic functions, we obtain that the equilibria of the model are locally stable when some suitable conditions are being satisfied. According to the comparison theorem and iteration technique, the globally asymptotic stability of the positive equilibrium is discussed. And, the sufficient conditions of the global stability to the trivial equilibrium and the boundary equilibrium are derived. The study shows that the prey refuge will enhance the density of the prey species, and it will decrease the density of predator species. Finally, some numerical simulations are carried out to show the efficiency of our main results.

46

Lozano-Ochoa, Enrique, Jorge Fernando Camacho, and Cruz Vargas-De-León. "Qualitative Stability Analysis of an Obesity Epidemic Model with Social Contagion." Discrete Dynamics in Nature and Society 2017 (2017): 1–12. http://dx.doi.org/10.1155/2017/1084769.

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We study an epidemiological mathematical model formulated in terms of an ODE system taking into account both social and nonsocial contagion risks of obesity. Analyzing first the case in which the model presents only the effect due to social contagion and using qualitative methods of the stability analysis, we prove that such system has at the most three equilibrium points, one disease-free equilibrium and two endemic equilibria, and also that it has no periodic orbits. Particularly, we found that when considering R0 (the basic reproductive number) as a parameter, the system exhibits a backward bifurcation: the disease-free equilibrium is stable when R0<1 and unstable when R0>1, whereas the two endemic equilibria appear from R0⁎ (a specific positive value reached by R0 and less than unity), one being asymptotically stable and the other unstable, but for R0>1 values, only the former remains inside the feasible region. On the other hand, considering social and nonsocial contagion and following the same methodology, we found that the dynamic of the model is simpler than that described above: it has a unique endemic equilibrium point that is globally asymptotically stable.

47

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 (April 25, 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 global stability of the coexistence equilibrium.

48

Naim, Mouhcine, and Fouad Lahmidi. "Analysis of a Deterministic and a Stochastic SIS Epidemic Model with Double Epidemic Hypothesis and Specific Functional Response." Discrete Dynamics in Nature and Society 2020 (May 26, 2020): 1–11. http://dx.doi.org/10.1155/2020/5362716.

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The purpose of this paper is to investigate the stability of a deterministic and stochastic SIS epidemic model with double epidemic hypothesis and specific nonlinear incidence rate. We prove the local asymptotic stability of the equilibria of the deterministic model. Moreover, by constructing a suitable Lyapunov function, we obtain a sufficient condition for the global stability of the disease-free equilibrium. For the stochastic model, we establish global existence and positivity of the solution. Thereafter, stochastic stability of the disease-free equilibrium in almost sure exponential and pth moment exponential is investigated. Finally, numerical examples are presented.

49

Shah, Nita H., Nisha Sheoran, and Ekta Jayswal. "Z-Control on COVID-19-Exposed Patients in Quarantine." International Journal of Differential Equations 2020 (June 19, 2020): 1–11. http://dx.doi.org/10.1155/2020/7876146.

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In this paper, a mathematical model for diabetic or hypertensive patients exposed to COVID-19 is formulated along with a set of first-order nonlinear differential equations. The system is said to exhibit two equilibria, namely, exposure-free and endemic points. The reproduction number is obtained for each equilibrium point. Local stability conditions are derived for both equilibria, and global stability is studied for the endemic equilibrium point. This model is investigated along with Z-control in order to eliminate chaos and oscillation epidemiologically showing the importance of quarantine in the COVID-19 environment.

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GIANNITSAROU, CHRYSSI. "E-STABILITY DOES NOT IMPLY LEARNABILITY." Macroeconomic Dynamics 9, no. 2 (April 2005): 276–87. http://dx.doi.org/10.1017/s1365100505040137.

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The concept of E-stability is widely used as a learnability criterion in studies of macroeconomic dynamics with adaptive learning. In this paper, it is demonstrated, via a counterexample, that E-stability generally does not imply learnability of rational expectations equilibria. The result indicates that E-stability may not be a robust device for equilibrium selection.