scholarly journals Asymptotic behavior of a three-species food chain model with time-varying delays

2021 ◽  
Author(s):  
Yuxiao Zhao ◽  
Linshan Wang ◽  
Yangfan Wang
Keyword(s):  
Asymptotic Behavior ◽  
Exponential Stability ◽  
Positive Solutions ◽  
Food Chain ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Chain Model ◽  
Time Varying ◽  
Razumikhin Technique ◽  
Food Chain Model

In this paper, a stochastic three-species food chain model with time-varying delays is focussed. The existence and the asymptotic behavior of global positive solutions to the model are discussed, and the sufficient conditions for the 1th moment practical exponential stability and the extinction of the model are given by using the Razumikhin technique and Lyapunov method.

Dynamics of a Food Chain Model with Two Infected Predators

2021 ◽  
Vol 31 (02) ◽  
pp. 2150019
Author(s):  
Xin-You Meng ◽  
Ni-Ni Qin ◽  
Hai-Feng Huo
Keyword(s):  
Food Chain ◽  
Disease Transmission ◽  
Sufficient Conditions ◽  
Geometric Approach ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Chain Model ◽  
Number Formula ◽  
Manifold Theory ◽  
Food Chain Model

In this paper, the dynamics of a three-species food chain model with two predators infected by an infectious disease is investigated. The positivity and boundedness of the system, the existence of the equilibria and the basic reproductive number are given. Sufficient conditions for the local stability of all equilibria are obtained by analyzing the corresponding characteristic equations. By constructing suitable Lyapunov functions and taking the geometric approach, the global stability of all equilibria is proved. According to the center manifold theory, this model undergoes the phenomenon of backward and forward bifurcations in a certain range of the basic reproductive number [Formula: see text]. By taking the disease transmission coefficient of predator as bifurcation parameter, Hopf bifurcation emerges in the neighborhood of the endemic equilibrium. Furthermore, the optimal control of the disease is discussed by the Pontryagin’s maximum principle. Various simulations are given to support the analytical results.

scholarly journals Global Stability for a Three-Species Food Chain Model in a Patchy Environment

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Hongli Li ◽  
Yaolin Jiang ◽  
Long Zhang ◽  
Zhidong Teng
Keyword(s):  
Food Chain ◽  
Sufficient Conditions ◽  
Coupled Systems ◽  
Positive Equilibrium ◽  
Chain Model ◽  
Patchy Environment ◽  
Globally Asymptotically Stable ◽  
Predator Species ◽  
Graph Theoretical Approach ◽  
Food Chain Model

We investigate a three-species food chain model in a patchy environment where prey species, mid-level predator species, and top predator species can disperse amongndifferent patches(n≥2). By using the method of constructing Lyapunov functions based on graph-theoretical approach for coupled systems, we derive sufficient conditions under which the positive equilibrium of this model is unique and globally asymptotically stable if it exists.

scholarly journals GLOBAL STABILITY OF A THREE-SPECIES FOOD-CHAIN MODEL WITH DIFFUSION AND NONLOCAL DELAYS

2011 ◽  
Vol 16 (3) ◽  
pp. 376-389 ◽  
Author(s):  
Xiao Zhang ◽  
Rui Xu ◽  
Zhe Li
Keyword(s):  
Steady State ◽  
Global Stability ◽  
Food Chain ◽  
Energy Function ◽  
Function Method ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Chain Model ◽  
Food Chain Model ◽  
Theoretical Results

In this paper, a three species reaction-diffusion food-chain system with nonlocal delays is investigated. Sufficient conditions are derived for the global stability of a positive steady state and boundary steady states of the system by using the energy function method. Numerical simulations are carried out to illustrate the theoretical results.

scholarly journals Dynamics of a Nonautonomous Leslie-Gower Type Food Chain Model with Delays

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Hongying Lu ◽  
Weiguo Wang
Keyword(s):  
Periodic Solution ◽  
Asymptotic Stability ◽  
Food Chain ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Chain Model ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Food Chain Model

A nonautonomous Leslie-Gower type food chain model with time delays is investigated. It is proved the general nonautonomous system is permanent and globally asymptotically stable under some appropriate conditions. Furthermore, if the system is periodic one, some sufficient conditions are established, which guarantee the existence, uniqueness, and global asymptotic stability of a positive periodic solution of the system. The conditions for the permanence, global stability of system, and the existence, uniqueness of positive periodic solution depend on delays; so, time delays are profitless.

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