Spatially nonhomogeneous patterns for a modified Leslie–Gower model with predator-taxis

Abstract

In this paper, we investigate a modified Leslie–Gower predator–prey model with predator-taxis under the Neumann boundary condition. Firstly, the boundness of solution and the global stability conditions of the positive equilibrium are performed. Secondly, we take predator-taxis sensitivity coefficient as a potential bifurcation parameter for Turing bifurcation and analyze multiple steady-state bifurcation thresholds. Then, we use weak nonlinear analysis to derive amplitude equations to determine the direction of Turing bifurcation on multiple time scales. Finally, numerical simulations check the theoretical analysis results well. It is found that the predator-taxis can induce the occurrence of nonhomogeneous steady-state solution in space.