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Cite Details

Aric Hagberg, Ehud Meron and Thierry Passot, "Phase dynamics of nearly stationary patterns in activator-inhibitor systems", Phys. Rev. E, vol. 61, no. 6, pp. 6471--6476, 2000

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 the Turing unstable regimes. Stability thresholds are obtained for the Eckhaus and the zigzag instabilities and for the transition to traveling waves. Neutral stability curves demonstrate the destabilization of stationary planar patterns at low wavenumbers to zigzag and traveling modes. Numerical solutions of the model system support the theoretical findings.

BibTeX Entry

@article{hagberg-2000-phase,
author = {Aric Hagberg and Ehud Meron and Thierry Passot},
title = {Phase dynamics of nearly stationary patterns in activator-inhibitor systems},
year = {2000},
urlpdf = {http://math.lanl.gov/~hagberg/Papers/phase/phase.pdf},
journal = {Phys. Rev. E},
volume = {61},
number = {6},
pages = {6471--6476}
}