Resumen de Spatiotemporal Dynamics in a Diffusive Predator–Prey System with Beddington–DeAngelis Functional Response

Xiang Ping Yan, Cun Hua Zhang

• This paper is concerned with a reaction–diffusion predator–prey system with a Beddington–DeAngelis functional response and subject to Neumann boundary conditions. The stability criteria and Turing instability conditions of the constant positive steady state of the system are provided. Some prior estimates, conditions to the nonexistence and the existence of non-constant positive steady-state solutions to the system are established and Turing patterns are also explored. The existence of spatially homogeneous and nonhomogeneous Hopf bifurcations of the constant positive equilibrium are discussed. Their achievements provide that the presence of the Beddington–DeAngelis functional response essentially increases the spatiotemporal complexity of the model and also leads to the appearance of Turing instability. Finally, some numerical tests are given to illustrate the theoretical findings.