Electronic Journal of Differential Equations, Vol. 2022 (2022), No. 37, pp. 1-15.

Title: Dynamical behavior in a reaction-diffusion system with prey-taxis
       
Authors: Yingwei Song (Northeastern Univ., Shenyang, China)
         Tie Zhang    (Northeastern Univ., Shenyang, China)
         Jinpeng Li (Univ. College London, London, UK)

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.

Submitted August 26, 2021. Published May 13, 2022.
Math Subject Classifications: 35B32, 35K57, 37L10.
Key Words: Reaction; diffusion; global solution; stability.