Bifurcation Analysis of a Diffusive Predator–Prey Model with Bazykin Functional Response

Abstract

This paper deals with a diffusive predator–prey model with Bazykin functional response. The parameter regions for the stability and instability of the unique constant steady state are derived. The Turing (diffusion-driven) instability which induces spatial inhomogeneous patterns, the existence of time-periodic orbits which produce temporal inhomogeneous patterns, the existence and nonexistence of nonconstant steady state positive solutions are proved. Numerical simulations are presented to verify and illustrate the theoretical results.