Phase Dynamics of Nearly Stationary Patterns in Activator-Inhibitor Systems

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. In the bistable case 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.

References in corpus (5)

• Pattern Formation in Dissipative Nonvariational Systems: The Effects of Front Bifurcations
• From Labyrinthine Patterns to Spiral Turbulence
• Complex Patterns in Reaction-Diffusion Systems: A Tale of Two Front Instabilities
• Interface Proliferation and the Growth of Labyrinths in a Reaction-Diffusion System
• General theory of instabilities for patterns with sharp interfaces in reaction-diffusion systems

Cited by in corpus (1)

• Six decades of the FitzHugh-Nagumo model: A guide through its spatio-temporal dynamics and influence across disciplines