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.

scholarly journals Global asymptotic stability in a periodic Lotka-Volterra system

1985 ◽  
Vol 27 (1) ◽  
pp. 66-72 ◽  
Author(s):  
K. Gopalsamy
Keyword(s):  
Periodic Solution ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Sufficient Conditions ◽  
Asymptotically Stable ◽  
Stable Periodic Solution ◽  
Volterra System ◽  
Periodic Coefficients ◽  
Globally Asymptotically Stable ◽  
Stable Periodic

AbstractA set of easily verifiable sufficient conditions are obtained for the existence of a globally asymptotically stable periodic solution in a Lotka-Volterra system with periodic coefficients.

Analysis of nonautonomous two species system in a polluted environment

2012 ◽  
Vol 62 (3) ◽  
Author(s):  
G. Samanta
Keyword(s):  
Periodic Solution ◽  
Population Growth ◽  
Asymptotic Behaviour ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Volterra Model ◽  
Asymptotically Stable ◽  
Polluted Environment ◽  
Globally Asymptotically Stable ◽  
Bounded Functions

AbstractIn this paper, a two-species nonautonomous Lotka-Volterra model of population growth in a polluted environment is proposed. Global asymptotic behaviour of this model by constructing suitable bounded functions has been investigated. It is proved that each population for competition, predation and cooperation systems respectively is uniformly persistent (permanent) under appropriate conditions. Sufficient conditions are derived to confirm that if each of competition, predation and cooperation systems respectively admits a positive periodic solution, then it is globally asymptotically stable.

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 asymptotic stability in an almost-periodic Lotka-Volterra system

1986 ◽  
Vol 27 (3) ◽  
pp. 346-360 ◽  
Author(s):  
K. Gopalsamy
Keyword(s):  
Periodic Solution ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Asymptotically Stable ◽  
Almost Periodic ◽  
Volterra System ◽  
Periodic Coefficients ◽  
Globally Asymptotically Stable

AbstractSufficient conditions are obtained for the existence of a globally asymptotically stable strictly positive (componentwise) almost-periodic solution of a Lotka-Volterra system with almost periodic coefficients.

scholarly journals Global Asymptotic Behavior of a Nonautonomous Competitor-Competitor-Mutualist Model

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Shengmao Fu ◽  
Fei Qu
Keyword(s):  
Asymptotic Behavior ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Time Dependent ◽  
Asymptotically Stable ◽  
Positive Periodic Solutions ◽  
Periodic Functions ◽  
Globally Asymptotically Stable ◽  
Periodic Model ◽  
Asymptotically Periodic

The global asymptotic behavior of a nonautonomous competitor-competitor-mutualist model is investigated, where all the coefficients are time-dependent and asymptotically approach periodic functions, respectively. Under certain conditions, it is shown that the limit periodic system of this asymptotically periodic model admits two positive periodic solutions(u1T,u2T,u3T),  (u1T,u2T,u3T)such thatuiT≤uiT  (i=1,2,3), and the sector{(u1,u2,u3):uiT≤ui≤uiT,  i=1,2,3}is a global attractor of the asymptotically periodic model. In particular, we derive sufficient conditions that guarantee the existence of a positive periodic solution which is globally asymptotically stable.

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.

Sign in / Sign up

Export Citation Format

Share Document