Dynamics of Partial Differential Equations

Volume 8 (2011)

Number 4

Multiple bifurcations and spatiotemporal patterns for a coupled two-cell Brusselator model

Pages: 363 – 384

DOI: http://dx.doi.org/10.4310/DPDE.2011.v8.n4.a4

Authors

Junjie Wei (Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang, China)

Wenjie Zuo (Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang, China)

Abstract

A coupled two-cell Brusselator model with diffusion effect subject to Neumann boundary condition is considered. Hopf bifurcations and global steady state bifurcations which bifurcate from the unique positive constant equilibrium point are investigated in detail. Meanwhile, Turing instability occurs when diffusion is present. Particularly, we show the existence of spatially inhomogeneous periodic solutions and non-constant steady state solutions, which exhibit rich spatiotemporal patterns in this coupled Brusselator system. Some numerical simulations are presented to illustrate the theoretical results obtained.

Keywords

coupled Brusselator model; diffusion; Hopf bifurcation; global steady state bifurcation; spatiotemporal pattern

2010 Mathematics Subject Classification

35-xx, 37-xx

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