Hopf bifurcation in a reaction-diffusion model with Degn-Harrison reaction scheme

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• 作者：Yaying Dong^a ; Shanbing Li^b ; ^{lishanbing2006@163.com" class="auth_mail" title="E-mail the corresponding author} ; Shunli Zhang^c
• 关键词：Degn&ndash ; Harrison reaction scheme ; Hopf bifurcation ; Bifurcation direction ; Stability
• 刊名：Nonlinear Analysis: Real World Applications
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：33
• 期：Complete
• 页码：284-297
• 全文大小：2600 K

文摘

In this paper, we consider a chemical reaction–diffusion model with Degn–Harrison reaction scheme under homogeneous Neumann boundary conditions. The existence of Hopf bifurcation to ordinary differential equation (ODE) and partial differential equation (PDE) models are derived, respectively. Furthermore, by using the center manifold theory and the normal form method, we establish the bifurcation direction and stability of periodic solutions. Finally, some numerical simulations are shown to support the analytical results, and to reveal new phenomenon on the Hopf bifurcation.