Phase dynamics of nearly stationary patterns in activator-inhibitor systems

被引：0

作者：

Hagberg, Aric ^{[1
]}

Meron, Ehud ^{[2
]}

Passot, Thierry ^{[3
,4
]}

机构：

[1] Center for Nonlinear Studies and T-7, Theoretical Division, Los Alamos National Laboratory, Los Alamos,NM,87545, United States

[2] Jacob Blaustein Institute for Desert Research, Physics Department, Ben-Gurion University, 84990, Israel

[3] Observatoire de la Côte d'Azur, Boîte Postale 4229, Nice Cedex 4,06304, France

[4] Department of Mathematics, University of Arizona, Tucson,AZ,85721, United States

来源：

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | 2000年 / 61卷 / 06期

关键词：

Condensed matter physics;

D O I：

暂无

中图分类号：

O64 [物理化学（理论化学）、化学物理学];

学科分类号：

070304 ; 081704 ;

摘要：

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. ©2000 The American Physical Society.

引用

页码：6471 / 6476

共 50 条

[1] Phase dynamics of nearly stationary patterns in activator-inhibitor systems
Hagberg, A
Meron, E
Passot, T
PHYSICAL REVIEW E, 2000, 61 (06): : 6471 - 6476
[2] Stable Patterns Generated by Activator-Inhibitor Systems
Jager, Edgar
Mathematical Medicine and Biology, 1986, 3 (03) : 179 - 190
[3] Regular patterns in dichotomically driven activator-inhibitor dynamics
Sailer, X.
Hennig, D.
Beato, V.
Engel, H.
Schimansky-Geier, L.
PHYSICAL REVIEW E, 2006, 73 (05):
[4] Complex nonlinear dynamics in subdiffusive activator-inhibitor systems
Datsko, B.
Gafiychuk, V.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2012, 17 (04) : 1673 - 1680
[5] COHERENCE RESONANCE IN EXCITABLE SYSTEMS: ACTIVATOR-INHIBITOR DYNAMICS
Stan, Cristina
Cristescu, Constantin P.
Alexandroaei, Dumitru
REVUE ROUMAINE DE CHIMIE, 2008, 53 (09) : 869 - +
[6] Dynamics and patterns of an activator-inhibitor model with cubic polynomial source
Yanqiu Li
Juncheng Jiang
Applications of Mathematics, 2019, 64 : 61 - 73
[7] DYNAMICS AND PATTERNS OF AN ACTIVATOR-INHIBITOR MODEL WITH CUBIC POLYNOMIAL SOURCE
Li, Yanqiu
Jiang, Juncheng
APPLICATIONS OF MATHEMATICS, 2019, 64 (01) : 61 - 73
[8] Turing patterns in network-organized activator-inhibitor systems
Nakao, Hiroya
Mikhailov, Alexander S.
NATURE PHYSICS, 2010, 6 (07) : 544 - 550
[9] The dynamics of a kinetic activator-inhibitor system
Ni, Wei-Ming
Suzuki, Kanako
Takagi, Izumi
JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 229 (02) : 426 - 465
[10] Degenerate Turing Bifurcation and the Birth of Localized Patterns in Activator-Inhibitor Systems
Villar-Sepulveda, Edgardo
Champneys, Alan
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 2023, 22 (03): : 1673 - 1709

← 1 2 3 4 5 →