Global asymptotical behavior of the Lengyel–Epstein reaction–diffusion system

The Lengyel–Epstein reaction–diffusion system of the CIMA reaction is revisited. We construct a Lyapunov function to show that the constant equilibrium solution is globally asymptotically stable when the feeding rate of iodide is small. We also show that for small spatial domains, all solutions even...

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Bibliographic Details
Published in:Applied mathematics letters 2009, Vol.22 (1), p.52-55
Main Authors: Yi, Fengqi, Wei, Junjie, Shi, Junping
Format: Article
Language:English
Subjects:
CIMA reaction
Exact sciences and technology
Global analysis, analysis on manifolds
Global asymptotical stability
Invariant rectangle
Lengyel–Epstein system
Lyapunov function
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary:The Lengyel–Epstein reaction–diffusion system of the CIMA reaction is revisited. We construct a Lyapunov function to show that the constant equilibrium solution is globally asymptotically stable when the feeding rate of iodide is small. We also show that for small spatial domains, all solutions eventually converge to a spatially homogeneous and time-periodic solution.
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2008.02.003