scholarly journals Existence and global attractivity of positive periodic solutions for a generalized predator–prey system with time delay

2006 ◽  
Vol 44 (1-2) ◽  
pp. 188-203 ◽  
Author(s):  
Zhengqiu Zhang ◽  
Huilan Wang
Keyword(s):  
Time Delay ◽  
Periodic Solutions ◽  
Global Attractivity ◽  
Positive Periodic Solutions ◽  
Predator Prey ◽  
Prey System ◽  
System With Time Delay

scholarly journals Existence of Positive Periodic Solutions for a Nonautonomous Generalized Predator-Prey System with Time Delay in Two-Patch Environment

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Huilan Wang ◽  
Zhengqiu Zhang ◽  
Weiping Zhou
Keyword(s):  
Periodic Solutions ◽  
Topological Degree ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Positive Periodic Solutions ◽  
Predator Prey ◽  
Prey System ◽  
System With Time Delay ◽  
Function Matrix

By using continuation theorem of coincidence degree theory, sufficient conditions of the existence of positive periodic solutions are obtained for a generalized predator-prey system with diffusion and delays. In this paper, we construct a V-function to make the prior estimation for periodic solutions, which makes the discussion more concise. Moreover, to compute the mapping's topological degree, a polynomial function matrix is constructed straightforwardly as a homotopic mapping for the generalized one, which improves the methods of computation on topological degree for a generalized mapping.

scholarly journals Global Attractivity of Positive Periodic Solution for a Delayed Predator-Prey System with Diffusion and Impulses

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Yuanfu Shao ◽  
Xiaolan Xie ◽  
Zhixiang Ju
Keyword(s):  
Periodic Solution ◽  
Numerical Analysis ◽  
Periodic Solutions ◽  
Lyapunov Functional ◽  
Global Attractivity ◽  
Positive Periodic Solution ◽  
Positive Periodic Solutions ◽  
Predator Prey ◽  
Prey System

By constructing a suitable Lyapunov functional, the global attractivity of positive periodic solutions for a delayed predator-prey system with diffusion and impulses is studied in this paper. Finally, an example and numerical analysis are given to show the effectiveness of the main results.

scholarly journals Periodic solutions of a two-species ratio-dependent predator-prey system with time delay in a two-patch environment

2003 ◽  
Vol 45 (2) ◽  
pp. 233-244 ◽  
Author(s):  
Zhengqiu Zhang ◽  
Zhicheng Wang
Keyword(s):  
Periodic Solution ◽  
Time Delay ◽  
Periodic Solutions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Positive Periodic Solution ◽  
Sufficient Condition ◽  
Predator Prey ◽  
Prey System ◽  
System With Time Delay

AbstractBy using the continuation theorem of coincidence degree theory, a sufficient condition is obtained for the existence of a positive periodic solution of a predator-prey diffusion system.

scholarly journals Multiple Positive Periodic Solutions for a Gilpin-Ayala Competition Predator-Prey System with Harvesting Terms

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Yongzhi Liao ◽  
Yongkun Li ◽  
Xiaoyan Dou
Keyword(s):  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Continuation Theorem ◽  
Coincidence Degree Theory ◽  
Positive Periodic Solutions ◽  
Mawhin’S Continuation Theorem ◽  
Predator Prey ◽  
Prey System

By applying Mawhin’s continuation theorem of coincidence degree theory, we study the existence of multiple positive periodic solutions for a Gilpin-Ayala competition predator-prey system with harvesting terms and obtain some sufficient conditions for the existence of multiple positive periodic solutions for the system under consideration. The result of this paper is completely new. An example is employed to illustrate our result.

DYNAMIC COMPLEXITIES OF HOLLING TYPE II FUNCTIONAL RESPONSE PREDATOR–PREY SYSTEM WITH DIGEST DELAY AND IMPULSIVE HARVESTING ON THE PREY

2009 ◽  
Vol 02 (02) ◽  
pp. 229-242 ◽  
Author(s):  
JIANWEN JIA ◽  
HUI CAO
Keyword(s):  
Time Delay ◽  
Functional Response ◽  
Impulsive Differential Equation ◽  
Global Attractivity ◽  
Sufficient Condition ◽  
Type Ii ◽  
Predator Prey ◽  
Prey System ◽  
Impulsive Harvesting ◽  
Type Ii Functional Response

In this paper, we introduce and study Holling type II functional response predator–prey system with digest delay and impulsive harvesting on the prey, which contains with periodically pulsed on the prey and time delay on the predator. We investigate the existence and global attractivity of the predator-extinction periodic solutions of the system. By using the theory on delay functional and impulsive differential equation, we obtain the sufficient condition with time delay and impulsive perturbations for the permanence of the system.

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