Turing instability of a predator-prey model with Beddington-DeAngelis functional response on a circular domain

In the present work, we are investigating the spatiotemporal dynamics predator-prey model with modified Leslie-Gower and Beddington-DeAngelis functional response. This model is given by a reaction diffusion system defined on a circular spatial domain. We prove the existence of critical lines of Hopf and Turing bifurcations in the circular spatial domain by using mathematical theory. In the end, we carry out numerical simulations to interpret how biological processes affect spatiotemporal pattern formation in a disc spatial domain and the role of the bifurcation parameter on the solutions of the model.