Turing instability in a modified cross-diffusion Leslie–Gower predator–prey model with Beddington–DeAngelis functional response

Abstract

Abstract In this paper, a modified cross-diffusion Leslie–Gower predator–prey model with the Beddington–DeAngelis functional response is studied. We use the linear stability analysis on constant steady states to obtain sufficient conditions for the occurrence of Turing instability and Hopf bifurcation. We show that the Turing instability and associated patterns are induced by the variation of parameters in the cross-diffusion term. Some numerical simulations are given to illustrate our results.

Keywords

• Modified Leslie–Gower model
• Beddington–DeAngelis functional response
• Turing instability
• Hopf bifurcation
• Cross-diffusion