The Effects of Varying Predator Dispersal Strength on Prey-Predator Dynamics with Refuge Process

The combined effects of (symmetric or asymmetric) dispersal and refuge mechanisms can have a significant impact on prey-predator dynamics. However, there remains a knowledge gap in concerning the incorporation of asymmetrical dispersal in the presence of prey refuges. Therefore, this paper aims to examine the influence of varying levels of asymmetrical (i.e., predator) dispersal on the interactions between prey and predators, as well as the role of prey refuges in facilitating species coexistence. The investigation begins by introducing an ordinary differential equation (ODE) model for the prey-predator system, which is subsequently extended to a partial differential equation (PDE) model. By conducting one-parameter bifurcation analysis on both models, the presence of transcritical and Hopf bifurcation points is established. Furthermore, the research delves into the spatio-temporal dynamics of the PDE model, capturing the intricate interactions between a specialized prey species and its predator. The focus is on examining the effects of different strengths of predator dispersal on the dynamics of the prey-predator system. The aim is to gain a comprehensive understanding of how predator dispersal influences the stability and persistence of the system, and to investigate the ecological implications of these dynamics in terms of prey-predator coexistence. Hence, the main findings of the research suggest that the increased levels of predator dispersal led to a wider range of prey refuges, supporting species coexistence. In conclusion, this study emphasises the critical importance of predator and prey dispersal dynamics in determining the key mechanisms that can promote species coexistence