Abstract
We study invasion fronts in a class of simple, two-species reaction-diffusion systems that occur as models for recurrent precipitation and undercooled liquids. We exhibit several different modes of front propagation: the invasion of an unstable homogeneous equilibrium can create persistent periodic patterns, transient patterns, or simply a homogeneous state. We give criteria that distinguish between these different modes of invasion, corroborate our predictions with numerical simulations, and point to a rich variety of more subtle phenomena and bifurcations.
Original language | English (US) |
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Pages (from-to) | 360-402 |
Number of pages | 43 |
Journal | SIAM Journal on Applied Dynamical Systems |
Volume | 10 |
Issue number | 1 |
DOIs | |
State | Published - 2011 |
Keywords
- Front propagation
- Liesegang patterns
- Pattern formation
- Phase-field system
- Pulled and pushed fronts