##
Drift bifurcations of relative equilibria and transitions of spiral waves.

* Nonlinearity * **12** (1999) 741-755.

** Peter Ashwin, Ian Melbourne and Matt Nicol **

** Abstract **

We consider dynamical systems that are equivariant under a noncompact Lie
group of symmetries and the drift of relative equilibria in such systems.
In particular, we investigate how the drift for a parametrized family of
normally hyperbolic relative equilibria can change character at what we call
a `drift bifurcation'.
To do this, we use results of Arnold to analyze parametrized families
of elements in the Lie algebra of the symmetry group.

We examine effects in physical space of such drift bifurcations
for planar reaction-diffusion systems and note that these effects can explain
certain aspects of the transition from rigidly rotating spirals to
rigidly propagating `retracting waves'.
This is a bifurcation observed in
numerical simulations of excitable media where the rotation rate of a family
of spirals slows down and gives way to a semi-infinite translating
wavefront.

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