Turing instability and spatially homogeneous Hopf bifurcation in a diffusive Brusselator system
Articles
Xiang-Ping Yan
Lanzhou Jiaotong University
Pan Zhang
Lanzhou Jiaotong University
Cun-Huz Zhang
Lanzhou Jiaotong University
Published 2020-07-01
https://doi.org/10.15388/namc.2020.25.17437
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Keywords

Brusselator reaction–diffusion system
local stability
Turing instability
spatially homogeneous Hopf bifurcation
normal form

How to Cite

YanX.-P., ZhangP. and ZhangC.-H. (2020) “Turing instability and spatially homogeneous Hopf bifurcation in a diffusive Brusselator system”, Nonlinear Analysis: Modelling and Control, 25(4), pp. 638–657. doi: 10.15388/namc.2020.25.17437.

Abstract

The present paper deals with a reaction–diffusion Brusselator system subject to the homogeneous Neumann boundary condition. When the effect of spatial diffusion is neglected, the local asymptotic stability and the detailed Hopf bifurcation of the unique positive equilibrium of the associated ODE system are analyzed. In the stable domain of the ODE system, the effect of spatial diffusion is explored, and local asymptotic stability, Turing instability and existence of Hopf bifurcation of the constant positive equilibrium are demonstrated. In addition, the direction of spatially homogeneous Hopf bifurcation and the stability of the spatially homogeneous bifurcating periodic solutions are also investigated. Finally, numerical simulations are also provided to check the obtained theoretical results.

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