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.