Attraction in Nonmonotone Planar Systems and Real-Life Models

Abstract

Let $$h:V\subset {\mathbb {R}}^{2}\longrightarrow {\mathbb {R}}^{2}$$ be an embedding. The aim of this paper is to analyze the dynamical behavior of h depending on the number of fixed points and 2-cycles, their local behaviors and the features of V. Our approach allows us to extend some celebrated results of the theory of monotone flows, namely the order interval trichotomy, for non-monotone maps. Moreover, we discuss several applications in classical models. In the particular case of the Ricker system, we recover some recent results deduced from computer assistance.