Hopf bifurcation for a delayed predator–prey diffusion system with Dirichlet boundary condition

Zhan-Ping Ma, Hai-Feng Huo and Hong Xiang

Applied Mathematics and Computation, 2017, vol. 311, issue C, 1-18

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.

Keywords: Predator–prey system; Diffusion; Time delay; Steady-state solution; Hopf bifurcation (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:311:y:2017:i:c:p:1-18

DOI: 10.1016/j.amc.2017.05.012

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