Abstract
We show that lattice dynamical systems naturally arise on infinite-dimensional invariant manifolds of reactiondiffusion equations with spatially periodic diffusive fluxes. The result connects wave-pinning phenomena in lattice differential equations and in reactiondiffusion equations in inhomogeneous media. The proof is based on a careful singular perturbation analysis of the linear part, where the infinite-dimensional manifold corresponds to an infinite-dimensional centre eigenspace.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 193-207 |
| Number of pages | 15 |
| Journal | Proceedings of the Royal Society of Edinburgh Section A: Mathematics |
| Volume | 139 |
| Issue number | 1 |
| DOIs | |
| State | Published - Feb 2009 |
Bibliographical note
Funding Information:This work was partly supported by the National Science Foundation through Grant nos NSF DMS-0504271 (A.S.) and NSF DMS-0513438 (E.V.).