Preprint No.
A-99-26
Claudia Wulff
Translational symmetry-breaking for spiral waves.
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 can not 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
Mathematics Subject Classification (MSC91): no
Language: ENG
Available:not
Contact: Wulff, Claudia; Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (wulff@math.fu-berlin.de)
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