Dynamics of a periodic predator-prey reaction-diffusion system in heterogeneous environments

Abstract

This paper is dedicated to investigating a predator-prey reaction-diffusion model with time-periodic, where all coefficient functions are both spatially and temporally heterogeneous. We rigorously characterize the properties of the principal eigenvalue and establish a precise relationship between the coefficient functions and the dynamics. Our results indicate that slow predator movement and short frequency of environmental periodic variations promote successful predator invasion. Conversely, reducing the predator mortality rate facilitates long-term coexistence of both populations. Additionally, we explore the asymptotic behaviors of positive periodic solutions when the diffusion coefficients are large or small, revealing the effects of diffusion on the invasion dynamics.