Phase dynamics of nearly stationary patterns in activator-inhibitor systems

Journal Article · Thu Jun 01 00:00:00 EDT 2000 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.61.6471· OSTI ID:20216772

Hagberg, Aric ^[1]; Meron, Ehud ^[2]; Passot, Thierry ^[3]

---

1. Center for Nonlinear Studies and T-7, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
2. The Jacob Blaustein Institute for Desert Research and the Physics Department, Ben-Gurion University, Sede Boker Campus 84990, (Israel)
3. Observatoire de la Cote d'Azur, Boite Postale 4229, 06304 Nice Cedex 4, (France)

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. (c) 2000 The American Physical Society.

• OSTI ID: 20216772
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 61, Issue 6; Other Information: PBD: Jun 2000; ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
PHASE TRANSFORMATIONS
REACTION KINETICS
INSTABILITY
THEORETICAL DATA