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 language | English (US) |
---|---|
Pages (from-to) | 457-483 |
Number of pages | 27 |
Journal | Nonlinearity |
Volume | 22 |
Issue number | 2 |
DOIs | |
State | Published - 2009 |