School of Computing and Mathematical Sciences,
Division of Mathematics,
Glasgow Caledonian University,
Cowcaddens Road,
Glasgow G4 OBA, UK
E-mail: fam@gcal.ac.uk

Multiple Hopf bifurcation and chaos in problems with symmetries

Multiple Hopf bifurcation in problems with $O(2)$ symmetry leads to the standing and the travelling wave solutions. Swapping the branches at this point is considered by studying the irreducible representation of group $O(2)\times S^1$. The torus-doubling cascade bifurcations are investigated and it is shown that direction reversing chaos can be obtained through a symmetry-increasing bifurcation.