Dynamics analysis of a chemical reaction–diffusion model subject to Degn–Harrison reaction scheme. (August 2019)

• Record Type: Journal Article
• Authors: Yan, Xiang-Ping; Chen, Jian-Ye; Zhang, Cun-Hua
• Is Part Of: Nonlinear analysis. Volume 48(2019)
• Page Start: 161
• Page End: 181
• Publication Date: 2019-08
• Subjects: Reaction–diffusion chemical model -- Degn–Harrison reaction scheme -- Local asymptotic stability -- Turing instability -- Hopf bifurcation -- Time-periodic pattern; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.01.005
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: A chemical reaction–diffusion model with Degn–Harrison reaction scheme and subject to homogeneous Neumann boundary condition is revisited in this article. Local asymptotic stability, Turing instability and existence of Hopf bifurcation for the only constant positive equilibrium solution are established by analyzing the relevant eigenvalue problem. In particular, a simplified explicit formula determining the properties of spatially homogeneous Hopf bifurcation is derived by employing the normal form method and the center manifold theorem for reaction–diffusion equations. Our formula here simplifies the existing one obtained in Dong et al. (2017). Numerical approximations are also carried out in order to check our theoretical predictions.