Bifurcation in a reaction-diffusion model with nonlocal delay effect and nonlinear boundary condition

In this paper, the existence, stability, and multiplicity of steady-state solutions and periodic solutions for a reaction-diffusion model with nonlocal delay effect and nonlinear boundary condition are investigated by using Lyapunov-Schmidt reduction. When the interior reaction term is weaker than the boundary reaction term, it is found that there is no Hopf bifurcation no matter how either of the interior reaction delay and the boundary reaction delay changes. When the interior reaction term is stronger than the boundary reaction term, it is the interior reaction delay instead of the boundary reaction delay that determines the existence of Hopf bifurcation. Moreover, the general results are illustrated by applications to models with either a single delay or bistable boundary condition. (c) 2021 Elsevier Inc. All rights reserved.

Automated summary

This study investigates the existence, stability, and multiplicity of steady-state solutions and periodic solutions for a reaction-diffusion model with nonlocal delay effect and nonlinear boundary condition using Lyapunov-Schmidt reduction. It is found that when the interior reaction term is weaker than the boundary reaction term, there is no Hopf bifurcation, while if the interior reaction term is stronger, the existence of Hopf bifurcation depends on the interior reaction delay. The general results are illustrated by applying models with either a single delay or bistable boundary condition.