Robustness of Liesegang patterns

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Abstract

We propose a conceptual analysis of stationary reaction-diffusion patterns with geometric spatial scaling laws as observed in Liesegang patterns. We give necessary and sufficient conditions for such patterns to occur in a robust fashion. The main ingredients are a skew-product structure in the kinetics, caused by irreversible chemical reactions, the existence of localized spikes and slowly decaying boundary layers. The proofs invoke the analysis of homoclinic orbits in orbit-flip position for spatial dynamics. In particular, we show that there exists a manifold of initial conditions that do not converge to the equilibrium but to the homoclinic orbit as a set.

Original languageEnglish (US)
Pages (from-to)457-483
Number of pages27
JournalNonlinearity
Volume22
Issue number2
DOIs
StatePublished - 2009

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