__Loss
of stability of cycling chaos__

__Rob Sturman__

Department of Applied Mathematics

University of Leeds, UK

A structurally stable heteroclinic cycle between equilibria in
symmetric systems is a well documented phenomenon. Similar cycling is also
possible between more complicated sets, such as chaotic saddles. We investigate
the bifurcation at which such `cycling chaos' gains/loses stability, and find
two different outcomes when cycling chaos is destroyed: either a plethora of
stable high-period periodic orbits, or chaotic dynamics intermittent to
invariant subspaces. Which one is seen depends on the dimension of the
connections between invariant subspaces.