NDLI: Translational Symmetry-Breaking for Spiral Waves

Content Provider	Springer Nature Link
Author	LeBlanc, V. G. Wulff, C.
Copyright Year	2000
Abstract	Spiral waves are observed in numerous physical situations, ranging from Belousov-Zhabotinsky (BZ) chemical reactions, to cardiac tissue, to slime-mold aggregates. Mathematical models with Euclidean symmetry have recently been developed to describe the dynamic behavior (for example, meandering) of spiral waves in excitable media. However, no physical experiment is ever infinite in spatial extent, so the Euclidean symmetry is only approximate. Experiments on spiral waves show that inhomogeneities can anchor spirals and that boundary effects (for example, boundary drifting) become very important when the size of the spiral core is comparable to the size of the reacting medium. Spiral anchoring and boundary drifting cannot be explained by the Euclidean model alone.In this paper, we investigate the effects on spiral wave dynamics of breaking the translation symmetry while keeping the rotation symmetry. This is accomplished by introducing a small perturbation in the five-dimensional center bundle equations (describing Hopf bifurcation from one-armed spiral waves) which is SO(2)-equivariant but not equivariant under translations. We then study the effects of this perturbation on rigid spiral rotation, on quasi-periodic meandering and on drifting.
Starting Page	569
Ending Page	601
Page Count	33
File Format	PDF
ISSN	09388974
Journal	Journal of Nonlinear Science
Volume Number	10
Issue Number	5
e-ISSN	14321467
Language	English
Publisher	Springer-Verlag
Publisher Date	2000-10-01
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Analysis Theoretical, Mathematical and Computational Physics Mechanics ApplicationMathematics/Computational Methods of Engineering Economic Theory
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Engineering Modeling and Simulation

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