Hopf bifurcation in a reaction–diffusion model with Degn–Harrison reaction scheme. (February 2017)

• Record Type: Journal Article
• Authors: Dong, Yaying; Li, Shanbing; Zhang, Shunli
• Is Part Of: Nonlinear analysis. Volume 33(2017)
• Page Start: 284
• Page End: 297
• Publication Date: 2017-02
• Subjects: Degn–Harrison reaction scheme -- Hopf bifurcation -- Bifurcation direction -- Stability; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.07.002
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: 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.