Dynamics analysis of a chemical reaction–diffusion model subject to Degn–Harrison reaction scheme

• Published in: Nonlinear analysis: real world applications Vol. 48; pp. 161 - 181
• Main Authors: Yan, Xiang-Ping, Chen, Jian-Ye, Zhang, Cun-Hua
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 01.08.2019; Elsevier BV
• Subjects: Boundary conditions; Chemical reactions; Degn–Harrison reaction scheme; Diffusion; Eigenvalues; Hopf bifurcation; Local asymptotic stability; Mathematical models; Organic chemistry; Reaction-diffusion equations; Reaction–diffusion chemical model; Stability; Time-periodic pattern; Turing instability; Degn–Harrison reaction scheme; Hopf bifurcation; Local asymptotic stability; Turing instability; Time-periodic pattern; Reaction–diffusion chemical model
• ISSN: 1468-1218; 1878-5719
• DOI: 10.1016/j.nonrwa.2019.01.005

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.