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)|
|Number of pages||15|
|Journal||Proceedings of the Royal Society of Edinburgh Section A: Mathematics|
|State||Published - Feb 2009|
Bibliographical noteFunding 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.).