Turing-Hopf bifurcation of a diffusive predator-prey model with Beddington-DeAngelis functional response and variable harvesting

This paper investigates the dynamics of a reaction-diffusion model with variable harvesting and Beddington-DeAngelis functional response. After analyzing the corresponding characteristic equation, we investigate the existence of both diffusion-driven Turing bifurcation and delay-induced Hopf bifurcation. Moreover, we obtain the normal form truncated to the third-order terms for the Turing-Hopf bifurcation on the center manifold and investigate the dynamical behaviors near the Turing-Hopf bifurcation point. Finally, numerical simulation is used to validate the conclusions of the theoretical analysis.