Bifurcations in a Diffusive Predator–Prey Model with Beddington–DeAngelis Functional Response and Nonselective Harvesting

Abstract

In this paper, we discuss the dynamics of a predator–prey model with Beddington–DeAngelis functional response and nonselective harvesting. By using the Lyapunov–Schmidt reduction, we obtain the existence of spatially nonhomogeneous steady-state solution. The stability and existence of Hopf bifurcation at the spatially nonhomogeneous steady-state solution with the change of a specific parameter are investigated by analyzing the distribution of the eigenvalues. We also get an algorithm for determining the bifurcation direction of the Hopf bifurcating periodic solutions near the nonhomogeneous steady-state solution. Finally, we show some numerical simulations to verify our analytical results.