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

AbstractIn 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−τ))−d(t)),when functional response function f is monotonic or nonmonotonic

Topological degree in the generalized gause prey-predator model

We consider a generalized Gause prey-predator model with T-periodic continuous coefficients. In the case where the Poincaré map P over time T is well defined, the result of the paper can be explained as follows: we locate a subset U of R2 such that the topological degree d(I-P,U) equals to +1. The novelty of the paper is that the later is done under only continuity and (some) monotonicity assumptions for the coefficients of the model. A suitable integral operator is used in place of the Poincaré map to cope with possible nonuniqueness of solutions. The paper, therefore, provides a new framework for studying the generalized Gause model with functional differential perturbations and multi-valued ingredients