Translational symmetry-breaking for spiral waves
type: Item
instance of: scholarly article
title: Translational symmetry-breaking for spiral waves
zbMATH Open document ID: 0969.37024
published in: Journal of Nonlinear Science
publication date: 2001-09-25T00:00:00Z
review text: This paper concerns small SO(2)-equivariant perturbations of SE(2)-equivariant reaction-diffusion systems of the type \[ \partial_t u(t,x)=d \Delta u(t,x) + f(u(t,x)) + \varepsilon g(|x|,u(t,0)),\quad x \in \mathbb R^2. \] In fact, the authors study a three dimensional and a five dimensional system of ordinary differential equations, which describe the dynamics (after a center manifold reduction) near normally hyperbolic relative equilibria and relative periodic orbits, respectively. The perturbation behavior of rigid spiral rotations, of epicycle-like motions of the spiral tip (quasi-periodic meandering) and of circular motions of the spiral tip superimposed with a linear drift (linear meandering) is investigated. The generic effects are: Stabilization of certain SO(2)-orbits of rotating waves or of modulated waves (which are determined by Melnikov-like functions) and drifting along these SO(2)-orbits (thereby introducing another frequency).
reviewed by: Lutz Recke
Mathematics Subject Classification ID: 37G40
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 37L20
Mathematics Subject Classification ID: 37C80
zbMATH DE Number: 1563278
zbMATH Keywords: spiral anchoring
zbMATH Keywords: boundary drifting
zbMATH Keywords: breaking of the translation symmetry while keeping the rotation symmetry
zbMATH Keywords: entrainment attractor
zbMATH Keywords: resonance attractor
author: Victor G. LeBlanc
author: Claudia Wulff
MaRDI profile type: Publication
full work available at URL: s003320010005
OpenAlex ID: W2078781300
DOI: 10.1007/S003320010005
Recommended article: Rotational symmetry breaking for spiral waves
Recommended article: Lattice Symmetry-Breaking Perturbations for Spiral Waves
Recommended article: Bifurcations and dynamics of spiral waves
Recommended article: Spiral Waves in Nonlocal Equations
Recommended article: Spiral wave dynamics
Recommended article: Dynamics of spiral waves in non-equilibrium media
Recommended article: Spiral Waves in Spatially Discrete λ-ω Systems
Recommended article: Symmetry breaking and the interaction of hyperbolic waves
Recommended article: ON BIFURCATIONS OF SPIRAL WAVES IN THE PLANE
Recommended article: Spirals and dislocations in wave-vortex systems
description: scientific article; zbMATH DE number 1563278