Existence of Multiple Positive Periodic Solutions of Delayed Predator-Prey Models with Functional Responses

Authors:
Xlaoling Hu;Guirong Liu;Jurang Yan
Affiliations:
Engineering College of Shanxi University Taiyuan, Shanxi 030013, P.R. China;Engineering College of Shanxi University Taiyuan, Shanxi 030013, P.R. China and School of Mathematical Sciences, Shanxi University Taiyuan, Shanxi 030006, P.R. China;Engineering College of Shanxi University Taiyuan, Shanxi 030013, P.R. China and School of Mathematical Sciences, Shanxi University Taiyuan, Shanxi 030006, P.R. China
Venue:
Computers & Mathematics with Applications
Year:
2006

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Abstract

In this paper, by applying the continuation theorem of coincidence degree theory, we establish some new criteria for the existence of multiple positive periodic solutions for the delayed predator-prey model.x^'(t)=x(t)(r(t)-a(t)x(t))-b(t)f(x(t))y(t),y^'(t)=y(t)(c(t)f(x(t-@t))-d(t)), when functional response function f is monotonic or nonmonotonic.