THE EFFECT OF DELAY ON A DIFFUSIVE PREDATOR-PREY SYSTEM WITH HOLLING III FUNCTIONAL RESPONSE AND PREY REFUGE

2016 ◽  
Vol 17 (3) ◽  
pp. 231-257
Author(s):  
Haoyu Ren ◽  
Xue Cheng ◽  
Ruizhi Yang
Keyword(s):  
Functional Response ◽  
Prey Refuge ◽  
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.

Dynamical Analysis of Prey Refuge in a Predator-Prey System with Rosenzweig Functional Response

2011 ◽  
Vol 271-273 ◽  
pp. 577-580
Author(s):  
Zhi Hui Ma ◽  
Shu Fan Wang ◽  
Wen Ting Wang
Keyword(s):  
Functional Response ◽  
Stability Property ◽  
Dynamical Analysis ◽  
Prey Refuge ◽  
Predator Prey ◽  
Prey System ◽  
Stabilizing Effect ◽  
The Stability ◽  
Prey Refuges

In this paper, we proposed a predator-prey system incorporating Rosenzweig functional response and prey refuges. We will consider the stability property of the equilibria. Our results show that refuges using by prey have stabilizing effect on the considered system.

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.

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