Coexistence and competitive exclusion in a time-periodic Lotka-Volterra competition-diffusion system

Abstract

The evolutionary impact of both temporal periodicity and spatial heterogeneity on population ecology is a challenging problem. Hutson et al. (2001) [12] and Bai et al. (2022) [2] studied the effects of diffusion rates on the dynamics of a time-periodic Lotka-Volterra competition-diffusion system with identical interspecific competition abilities. In this paper, we consider the case of different interspecific competition coefficients. The obtained results can be divided into two groups. The first part focuses on the interplay between the diffusion intensities and the interspecific competition coefficients on the dynamics in the weak competition case. We provide some sufficient conditions on coexistence and competitive exclusion. The second part considers the dynamics for fixed diffusion coefficients and varying competition coefficients. We not only provide a complete classification on the dynamics when one of the interspecific competition coefficients is small, but also show the multiple coexistence periodic patterns by applying the bifurcation method.