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

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),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−τ))−d(t)),y′(t)=y(t)(c(t)f(x(t−τ))−d(t)),when functional response function f is monotonic or nonmonotonic.