scholarly journals Permanence and Global Attractivity of the Discrete Predator-Prey System with Hassell-Varley-Holling III Type Functional Response

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Runxin Wu ◽  
Lin Li
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Function ◽  
Difference Equation ◽  
Functional Response ◽  
Comparison Theorem ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Prey System

By constructing a suitable Lyapunov function and using the comparison theorem of difference equation, sufficient conditions which ensure the permanence and global attractivity of the discrete predator-prey system with Hassell-Varley-Holling III type functional response are obtained. An example together with its numerical simulation shows that the main results are verifiable.

scholarly journals Permanence and Global Attractivity of Discrete Predator-Prey System with Hassell-Varley Type Functional Response

2009 ◽  
Vol 2009 ◽  
pp. 1-17 ◽  
Author(s):  
Runxin Wu ◽  
Lin Li
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Function ◽  
Difference Equation ◽  
Functional Response ◽  
Comparison Theorem ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Prey System

By constructing a suitable Lyapunov function and using the comparison theorem of difference equation, sufficient conditions which ensure the permanence and global attractivity of the discrete predator-prey system with Hassell-Varley type functional response are obtained. Example together with its numerical simulation shows that the main results are verifiable.

EXISTENCE AND GLOBAL ATTRACTIVITY OF A POSITIVE PERIODIC SOLUTION FOR A NON-AUTONOMOUS PREDATOR-PREY MODEL UNDER VIRAL INFECTION

2009 ◽  
Vol 02 (04) ◽  
pp. 419-442 ◽  
Author(s):  
FENGYAN ZHOU
Keyword(s):  
Numerical Simulation ◽  
Periodic Solution ◽  
Lyapunov Function ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Positive Periodic Solution ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System

A new non-autonomous predator-prey system with the effect of viruses on the prey is investigated. By using the method of coincidence degree, some sufficient conditions are obtained for the existence of a positive periodic solution. Moreover, with the help of an appropriately chosen Lyapunov function, the global attractivity of the positive periodic solution is discussed. In the end, a numerical simulation is used to illustrate the feasibility of our results.

scholarly journals Dynamics Behaviors of a Discrete Ratio-Dependent Predator-Prey System with Holling Type III Functional Response and Feedback Controls

2008 ◽  
Vol 2008 ◽  
pp. 1-19 ◽  
Author(s):  
Jinghui Yang
Keyword(s):  
Lyapunov Function ◽  
Functional Response ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Feedback Controls ◽  
Predator Species ◽  
Predator Prey ◽  
Type Iii ◽  
Prey System ◽  
Ratio Dependent

A ratio-dependent predator-prey system with Holling type III functional response and feedback controls is proposed. By constructing a suitable Lyapunov function and using the comparison theorem of difference equation, sufficient conditions which ensure the permanence and global attractivity of the system are obtained. After that, under some suitable conditions, we show that the predator speciesywill be driven to extinction. Examples together with their numerical simulations show that the main results are verifiable.

scholarly journals Dynamic behaviors of a nonautonomous predator–prey system with Holling type II schemes and a prey refuge

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yumin Wu ◽  
Fengde Chen ◽  
Caifeng Du
Keyword(s):  
Lyapunov Function ◽  
Differential Equations ◽  
Comparison Theorem ◽  
Sufficient Conditions ◽  
Oscillation Theory ◽  
Type Ii ◽  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System

AbstractIn this paper, we consider a nonautonomous predator–prey model with Holling type II schemes and a prey refuge. By applying the comparison theorem of differential equations and constructing a suitable Lyapunov function, sufficient conditions that guarantee the permanence and global stability of the system are obtained. By applying the oscillation theory and the comparison theorem of differential equations, a set of sufficient conditions that guarantee the extinction of the predator of the system is obtained.

Harvesting Analysis of a Predator-Prey System with Functional Response

2013 ◽  
Vol 805-806 ◽  
pp. 1957-1961
Author(s):  
Ting Wu
Keyword(s):  
Numerical Simulation ◽  
Equilibrium Point ◽  
Functional Response ◽  
Sufficient Conditions ◽  
Optimal Harvesting ◽  
Predator Prey ◽  
Optimal Harvesting Policy ◽  
Prey System ◽  
The Stability ◽  
Maximal Principle

In this paper, a predator-prey system with functional response is studied,and a set of sufficient conditions are obtained for the stability of equilibrium point of the system. Moreover, optimal harvesting policy is obtained by using the maximal principle,and numerical simulation is applied to illustrate the correctness.

Permanence of a Predator-Prey System with Beddington-DeAngelis Functional Response

2013 ◽  
Vol 772 ◽  
pp. 839-843
Author(s):  
Ting Wu
Keyword(s):  
Functional Response ◽  
Comparison Theorem ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Prey System

In this paper, a Impulsive predator-prey system with Beddington-DeAngelis functional response is studied. By applying the comparison theorem of impulsive, sufficient conditions for the permanence of the system are obtained.

scholarly journals Almost Periodic Sequence Solutions of a Discrete Predator-Prey System with Beddington-DeAngelis Functional Response

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Zengji Du ◽  
Wenbin Li
Keyword(s):  
Periodic Solution ◽  
Lyapunov Function ◽  
Functional Response ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Periodic Sequence ◽  
Asymptotically Stable ◽  
Almost Periodic ◽  
Predator Prey ◽  
Prey System

This paper considers a discrete predator-prey system with Beddington-DeAngelis functional response. Sufficient conditions are obtained for the existence of the almost periodic solution which is uniformly asymptotically stable by constructing a Lyapunov function.

scholarly journals On the Dynamics of a Nonautonomous Predator-Prey Model with Hassell-Varley Type Functional Response

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Yan Zhang ◽  
Shujing Gao ◽  
Kuangang Fan
Keyword(s):  
Lyapunov Function ◽  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Incidence Rate ◽  
Functional Response ◽  
Global Attractivity ◽  
Migratory Birds ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Predator Prey Model

The dynamic behaviors of a nonautonomous system for migratory birds with Hassell-Varley type functional response and the saturation incidence rate are studied. Under quite weak assumptions, some sufficient conditions are obtained for the permanence and extinction of the disease. Moreover, the global attractivity of the model is discussed by constructing a Lyapunov function. Numerical simulations which support our theoretical analysis are also given.

scholarly journals Permanence and Global Attractivity of a Delayed Discrete Predator-Prey System with General Holling-Type Functional Response and Feedback Controls

2008 ◽  
Vol 2008 ◽  
pp. 1-17 ◽  
Author(s):  
Lijuan Chen ◽  
Junyan Xu ◽  
Zhong Li
Keyword(s):  
Periodic Solution ◽  
Functional Response ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Feedback Controls ◽  
Predator Prey ◽  
Prey System ◽  
Holling Type Functional Response

This paper discusses a delayed discrete predator-prey system with general Holling-type functional response and feedback controls. Firstly, sufficient conditions are obtained for the permanence of the system. After that, under some additional conditions, we show that the periodic solution of the system is global stable.

scholarly journals Permanence of a Discrete Predator-Prey Systems with Beddington-DeAngelis Functional Response and Feedback Controls

2008 ◽  
Vol 2008 ◽  
pp. 1-8 ◽  
Author(s):  
Xuepeng Li ◽  
Wensheng Yang
Keyword(s):  
Difference Equation ◽  
Functional Response ◽  
Comparison Theorem ◽  
Sufficient Conditions ◽  
Feedback Controls ◽  
Predator Prey

We propose a discrete predator-prey systems with Beddington-DeAngelis functional response and feedback controls. By applying the comparison theorem of difference equation, sufficient conditions are obtained for the permanence of the system.

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