Abstract
A delayed predator–prey diffusion system with Beddington–DeAngelis functional response under Dirichlet boundary condition is investigated. The existence and stability of the positive spatially nonhomogeneous steady-state solution are obtained via the implicit function theorem. Moreover, taking feedback time delay τ as the bifurcation parameter, Hopf bifurcation near the positive steady-state solution is proved to occur at a sequence of critical values, we can show that feedback time delay can induce nonhomogeneous periodic oscillatory patterns. The direction of Hopf bifurcation is forward when parameter m in model (1.2) is sufficiently large. Numerical simulations and numerical solutions are presented to illustrate our theoretical results.
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