Existence of Positive Periodic Solutions for Difference Equations of a Ratio-Dependent Predator-Prey System

2012 ◽  
Author(s):  
Wei Guo
Keyword(s):  
Periodic Solutions ◽  
Difference Equations ◽  
Positive Periodic Solutions ◽  
Predator Prey ◽  
Prey System ◽  
Ratio Dependent

scholarly journals Double Periodic Solutions for a Ratio-Dependent Predator-Prey System with Harvesting Terms on Time Scales

2009 ◽  
Vol 2009 ◽  
pp. 1-12 ◽  
Author(s):  
Zhenjie Liu
Keyword(s):  
Periodic Solutions ◽  
Time Scales ◽  
Difference Equations ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Discrete Models ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Ratio Dependent

We investigate a nonautonomous ratio-dependent predator-prey model with Beddington-DeAngelis functional response and multiple harvesting (or exploited) terms on time scales. By means of using a continuation theorem based on coincidence degree theory, we obtain sufficient criteria for the existence of at least two periodic solutions for the system. Moreover, when the time scale𝕋is chosen asℝorℤ, the existence of the periodic solutions of the corresponding continuous and discrete models follows. Therefore, the methods are unified to provide the existence of the desired solutions for the continuous differential equations and discrete difference equations.

scholarly journals On a Generalized Discrete Ratio-Dependent Predator-Prey System

2009 ◽  
Vol 2009 ◽  
pp. 1-22 ◽  
Author(s):  
Yong-Hong Fan ◽  
Lin-Lin Wang
Keyword(s):  
Periodic Solutions ◽  
Functional Response ◽  
Comparison Theorem ◽  
Continuous System ◽  
Discrete Systems ◽  
Positive Periodic Solutions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Ratio Dependent

Verifiable criteria are established for the permanence and existence of positive periodic solutions of a delayed discrete predator-prey model with monotonic functional response. It is shown that the conditions that ensure the permanence of this system are similar to those of its corresponding continuous system. And the investigations generalize some well-known results. In particular, a more acceptant method is given to study the bounded discrete systems rather than the comparison theorem.

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.

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