Phase dynamics of nearly stationary patterns in activator-inhibitor systems

Aric Hagberg, Ehud Meron, Thierry Passot

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

The slow dynamics of nearly stationary patterns in a FitzHugh-Nagumo model are studied using a phase dynamics approach. A Cross-Newell phase equation describing slow and weak modulations of periodic stationary solutions is derived. The derivation applies to the bistable, excitable, and Turing unstable regimes. In the bistable case stability thresholds are obtained for the Eckhaus and zigzag instabilities and for the transition to traveling waves. Neutral stability curves demonstrate the destabilization of stationary planar patterns at low wave numbers to zigzag and traveling modes. Numerical solutions of the model system support the theoretical findings.

Original languageEnglish
Pages (from-to)6471-6476
Number of pages6
JournalPhysical Review E
Volume61
Issue number6
DOIs
StatePublished - 1 Jan 2000

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