Instability and Pattern Formation in Three-Species Food Chain Model via Holling Type II Functional Response on a Circular Domain

Abstract

This paper is devoted to the study of food chain predator–prey model. This model is given by a reaction–diffusion system defined on a circular spatial domain, which includes three-state variables namely, prey and intermediate predator and top predator and incorporates the Holling type II and a modified Leslie–Gower functional response. The aim of this paper is to investigate theoretically and numerically the asymptotic behavior of the interior equilibrium of the model. The local and global stabilities of the positive steady-state solution and the conditions that enable the occurrence of Hopf bifurcation and Turing instability in the circular spatial domain are proved. In the end, we carry out numerical simulations to illustrate how biological processes can affect spatiotemporal pattern formation in a disc spatial domain and different types of spatial patterns with respect to different time steps and diffusion coefficients are obtained.