Dynamical behavior in a reaction-diffusion system with prey-taxis

Abstract

In this article, we study a diffusive predator-prey system with prey-taxis under homogeneous Neumann boundary conditions. We establish the existence and boundedness of nonnegative global solutions. Through comparison with the system without prey-taxis, we find that the positive constant equilibrium remains stable for positive prey-taxis, while negative prey-taxis makes it unstable.