Journal
NONLINEARITY
Volume 22, Issue 2, Pages 457-483Publisher
IOP Publishing Ltd
DOI: 10.1088/0951-7715/22/2/012
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Funding
- National Science Foundation [NSF-DMS-0806614]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0806614] Funding Source: National Science Foundation
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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.
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