Stability Analysis of a Diffusive Ratio-Dependent Predator-Prey Model with Nonlocal Perception

Abstract

In this paper, we propose a diffusive ratio-dependent predator-prey model with a nonlocal perceptual term. We first discuss the well-posedness of solutions. Then for the model without the nonlocal perception term, we obtain stability conditions of the spatially homogeneous steady state. Under these conditions, when considering the effects of nonlocal perception, our result indicates that if the system without nonlocal perception term is stable, and even after introducing nonlocal perception term, the system remains stable. However, if the system without nonlocal perception term is unstable, and the introduction of nonlocal perception term will make the system become stable.