Existence of Positive Periodic Solutions for Nonautonomous Predator-prey Systems with Discrete and Continuously Distributed Delays

2007 ◽  
Vol 23 (1) ◽  
pp. 39-48
Author(s):  
Yan Lv ◽  
Wei Lv ◽  
Jian-hua Sun
Keyword(s):  
Periodic Solutions ◽  
Distributed Delays ◽  
Positive Periodic Solutions ◽  
Predator Prey

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 Periodic Neutral Lotka-Volterra System with Distributed Delays and Impulses

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
Zhenguo Luo ◽  
Liping Luo
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Distributed Delays ◽  
Positive Periodic Solutions ◽  
Volterra System

By using a fixed-point theorem of strict-set-contraction, we investigate the existence of positive periodic solutions for a class of the following impulsive neutral Lotka-Volterra system with distributed delays:xi′(t)=xi(t)[ri(t)-∑j=1naij(t)xj(t)-∑j=1n‍bij(t)∫-τij0‍fij(ξ)xj(t+ξ)dξ-∑j=1n‍cij(t)∫-σij0‍gij(ξ)xj′(t+ξ)dξ],  Δxi(tk)=-Iik(xi(tk)),  i=1,2,…,n,  k=1,2,….Some verifiable criteria are established easily.

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