Non-local interaction effects in models of interacting populations

Abstract

We consider a couple of models for the dynamics of the populations of two interacting species, inspired by Lotka–Volterra’s classical equations. The main feature of this work is that the interaction terms are non local and the interactions occur within a bounded range. These terms include the competitive intraspecific interaction among individuals and the interspecific terms for which we consider two cases: Competition and predation. The results show that not only the non-locality induces spatial structures but also allows for the survival of the species when due to predation or the competitive exclusion extinction was expected, and even promotes spatio-temporal patterns not linked to eventual temporal oscillations in the local case. In this work, we also explore some interesting details about the behavior of the population dynamics that shows spatial patterns that interfere in a way that leads to non-trivial results. In this way, we complement and extend some results obtained in previous works.