Diffusion-driven instability and bifurcation in the Lengyel–Epstein system

Lengyel–Epstein reaction–diffusion system of the CIMA reaction is considered. We derive the precise conditions on the parameters so that the spatial homogenous equilibrium solution and the spatial homogenous periodic solution become Turing unstable or diffusively unstable. We also perform a detailed...

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Bibliographic Details
Published in:Nonlinear analysis: real world applications 2008-07, Vol.9 (3), p.1038-1051
Main Authors: Yi, Fengqi, Wei, Junjie, Shi, Junping
Format: Article
Language:English
Subjects:
Hopf bifurcation
Lengyel–Epstein system
The CIMA reaction
Turing diffusion-driven instability
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Summary:Lengyel–Epstein reaction–diffusion system of the CIMA reaction is considered. We derive the precise conditions on the parameters so that the spatial homogenous equilibrium solution and the spatial homogenous periodic solution become Turing unstable or diffusively unstable. We also perform a detailed Hopf bifurcation analysis to both the ODE and PDE models, and derive conditions for determining the bifurcation direction and the stability of the bifurcating periodic solution.
ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2007.02.005