The global stability of predator-prey system of Gause-type with Holling III functional response

2000 ◽  
Vol 5 (3) ◽  
pp. 271-277
Author(s):  
Feng Jian-wen ◽  
Zen Xian-wu
Keyword(s):  
Global Stability ◽  
Functional Response ◽  
Predator Prey ◽  
Prey System ◽  
Holling Iii Functional Response

scholarly journals Qualitative Analysis for a Predator Prey System with Holling Type III Functional Response and Prey Refuge

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Xia Liu ◽  
Yepeng Xing
Keyword(s):  
Qualitative Analysis ◽  
Global Stability ◽  
Numerical Simulations ◽  
Functional Response ◽  
Limit Cycle ◽  
Positive Equilibrium ◽  
Prey Refuge ◽  
Predator Prey ◽  
Prey System ◽  
Holling Iii Functional Response

A predator prey system with Holling III functional response and constant prey refuge is considered. By using the Dulac criterion, we discuss the global stability of the positive equilibrium of the system. By transforming the system to a Liénard system, the conditions for the existence of exactly one limit cycle for the system are given. Some numerical simulations are presented.

scholarly journals On a Periodic Predator-Prey System with Holling III Functional Response and Stage Structure for Prey

2010 ◽  
Vol 2010 ◽  
pp. 1-12
Author(s):  
Xiangzeng Kong ◽  
Zhiqin Chen ◽  
Li Xu ◽  
Wensheng Yang
Keyword(s):  
Functional Response ◽  
Prey Species ◽  
Necessary Conditions ◽  
Stage Structure ◽  
Predator Prey ◽  
Prey System ◽  
Sufficient And Necessary Conditions ◽  
Holling Iii Functional Response

We propose and study the permanence of the following periodic Holling III predator-prey system with stage structure for prey and both two predators which consume immature prey. Sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained.

scholarly journals Dynamic Behaviors of a Nonautonomous Discrete Predator-Prey System Incorporating a Prey Refuge and Holling Type II Functional Response

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Yumin Wu ◽  
Fengde Chen ◽  
Wanlin Chen ◽  
Yuhua Lin
Keyword(s):  
Global Stability ◽  
Numerical Simulations ◽  
Functional Response ◽  
Sufficient Conditions ◽  
Type Ii ◽  
Prey Refuge ◽  
Predator Species ◽  
Predator Prey ◽  
Prey System ◽  
Type Ii Functional Response

A nonautonomous discrete predator-prey system incorporating a prey refuge and Holling type II functional response is studied in this paper. A set of sufficient conditions which guarantee the persistence and global stability of the system are obtained, respectively. Our results show that if refuge is large enough then predator species will be driven to extinction due to the lack of enough food. Two examples together with their numerical simulations show the feasibility of the main results.

scholarly journals Boundedness and Global Stability for a Predator-Prey System with the Beddington-DeAngelis Functional Response

2010 ◽  
Vol 2010 ◽  
pp. 1-24 ◽  
Author(s):  
Wahiba Khellaf ◽  
Nasreddine Hamri
Keyword(s):  
Global Stability ◽  
Functional Response ◽  
Qualitative Behavior ◽  
Uniform Persistence ◽  
Boundedness Of Solutions ◽  
Predator Prey ◽  
Interior Equilibrium ◽  
Prey System ◽  
Predator Prey Models ◽  
Type Ii Functional Response

We study the qualitative behavior of a class of predator-prey models with Beddington-DeAngelis-type functional response, primarily from the viewpoint of permanence (uniform persistence). The Beddington-DeAngelis functional response is similar to the Holling type-II functional response but contains a term describing mutual interference by predators. We establish criteria under which we have boundedness of solutions, existence of an attracting set, and global stability of the coexisting interior equilibrium via Lyapunov function.

Global Stability of a Non-Smooth Predator–Prey System with Holling I Functional Response and Refuge Effect

2014 ◽  
Vol 595 ◽  
pp. 283-288 ◽  
Author(s):  
Yuan Tian ◽  
Hai Ting Sun ◽  
Yu Xia He
Keyword(s):  
Global Stability ◽  
Functional Response ◽  
Tangent Point ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Refuge Effect ◽  
Prey System ◽  
Trivial Equilibrium ◽  
The Stability ◽  
Regular Equilibrium

This paper analyses the dynamics of a non-smooth predator-prey model with refuge effect, where the functional response is taken as Holling I type. To begin with, some preliminaries and the existence of regular, virtual, pseudo-equilibrium and tangent point are established. Then, the stability of trivial equilibrium and predator free equilibrium is discussed. Furthermore, it is shown that the regular equilibrium and the pseudo-equilibrium cannot coexist. Finally, the conclusion is given.

Sign in / Sign up

Export Citation Format

Share Document