Stability and Bifurcation of a Delayed Reaction–Diffusion Model with Robin Boundary Condition in Heterogeneous Environment

Author:

Li Chaochao1,Guo Shangjiang1ORCID

Affiliation:

1. School of Mathematics and Physics, China University of Geosciences, Wuhan, Hubei 430074, P. R. China

Abstract

In this paper, we investigate a reaction–diffusion model with delay and Robin boundary condition in heterogeneous environment. The existence, multiplicity and stability of spatially nonhomogeneous steady-state solutions and periodic solutions are studied by employing the Lyapunov–Schmidt reduction method. Moreover, the Hopf bifurcation direction is derived. It is observed that Robin boundary condition plays a crucial role in the Hopf bifurcation. More precisely, when the boundary effect is stronger than the interaction of the species within the region, there is no Hopf bifurcation no matter how the time delay [Formula: see text] changes. Finally, we illustrate our general theoretical results by an application to the Nicholson’s blowflies model.

Funder

National Natural Science Foundation of China

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Symmetry-breaking bifurcations in a delayed reaction–diffusion equation;Zeitschrift für angewandte Mathematik und Physik;2023-03-09

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