Topological degree in the generalized gause prey-predator model

Abstract

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.