Multiple positive periodic solutions for an n-species competition predator-prey system on time scales

2012 ◽  
Vol 42 (1-2) ◽  
pp. 259-281 ◽  
Author(s):  
Dongshu Wang
Keyword(s):  
Periodic Solutions ◽  
Time Scales ◽  
Species Competition ◽  
Positive Periodic Solutions ◽  
Predator Prey ◽  
Prey System

Global Dynamics of a Delayed n + m-Species Competition Predator-Prey System on Time Scales

2015 ◽  
Vol 65 (3) ◽  
Author(s):  
Dongshu Wang
Keyword(s):  
Global Existence ◽  
Time Scales ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Global Dynamics ◽  
Species Competition ◽  
Positive Periodic Solutions ◽  
Predator Prey ◽  
Prey System ◽  
Holling Iii Functional Response

AbstractIn this paper, we consider a delayed n + m-species competition predator-prey system on time scales with Holling III functional response and multiple exploited (or harvesting) terms. By using the continuation theorem based on Gaines and Mawhin’s coincidence degree theory, easily verifiable criteria are established for global existence of multiple positive periodic solutions for the above 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.

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.

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