scholarly journals Multiple positive periodic solutions of a delayed discrete predator–prey system with type IV functional responses

2007 ◽  
Vol 20 (10) ◽  
pp. 1031-1038 ◽  
Author(s):  
Weipeng Zhang ◽  
Deming Zhu ◽  
Ping Bi
Keyword(s):  
Periodic Solutions ◽  
Positive Periodic Solutions ◽  
Functional Responses ◽  
Predator Prey ◽  
Type Iv ◽  
Prey System

scholarly journals Multiple Periodic Solutions of Delayed Predator-Prey Systems with Type IV Functional Responses on Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Shengbin Yu ◽  
Haihui Wu ◽  
Jiangbin Chen
Keyword(s):  
Periodic Solutions ◽  
Time Scales ◽  
Coincidence Degree ◽  
Continuation Theorem ◽  
Positive Periodic Solutions ◽  
Functional Responses ◽  
Predator Prey ◽  
Type Iv ◽  
Multiple Periodic Solutions

With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, easily verifiable criteria are established for the existence of multiple positive periodic solutions of delayed predator-prey systems with type IV functional responses on time scales. Our results not only unify the existing ones but also widen the range of applications.

scholarly journals Existence of Positive Periodic Solutions for a Predator-Prey System of Holling Type IV Function Response with Mutual Interference and Impulsive Effects

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Haidong Liu ◽  
Fanwei Meng
Keyword(s):  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Mutual Interference ◽  
Impulsive Effects ◽  
Positive Periodic Solutions ◽  
Predator Prey ◽  
Type Iv ◽  
Prey System ◽  
Predator Prey Models

We investigate the existence of periodic solutions for a predator-prey system with Holling function response and mutual interference. Our model is more general than others since it has both Holling type IV function and impulsive effects. With some new analytical tricks and the continuation theorem in coincidence degree theory proposed by Gaines and Mawhin, we obtain a set of sufficient conditions on the existence of positive periodic solutions for such a system. In addition, in the remark, we point out some minor errors which appeared in the proof of theorems in some published papers with relevant predator-prey models. An example is given to illustrate our results.

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.

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.

Sign in / Sign up

Export Citation Format

Share Document