Lattice differential equations embedded into reaction-diffusion systems

Arnd Scheel, Erik S. Van Vleck

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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 languageEnglish (US)
Pages (from-to)193-207
Number of pages15
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
Issue number1
StatePublished - 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.).

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