Global dynamics on a circular domain of a diffusion predator-prey model with modified Leslie-Gower and Beddington-DeAngelis functional type

In this paper, we present a predator-prey model with modified Leslie-Gower and Beddington-DeAngelis functional response. The model is governed by a two dimensional reaction diffusion system defined on a disc domain. The conditions of boundedness, existence of a positively invariant and attracting set are proved. Sufficient conditions of local and global stability of the positive steady state are established. In the end, we carry out some numerical simulations in order to illustrate our theoretical results and to interpret how biological processes affect spatio-temporal pattern formation.