WAVES ARISING FROM MODE INTERACTIONS IN PROBLEMS WITH O(2) SYMMETRY

Abstract

Codimension-two non-linear interaction of the symmetry preserving and the symmetry breaking Hopf bifurcations on a circle of $\Z_2$ symmetric steady states in systems with$O(2)$ symmetryis considered. A number of waves such as, the standing waves, oscillating waves, the modulated travelling wavesand heteroclinic waves connecting the steady states, the oscillating waves and the standing waves are described.The resulting waves are illustrated by considering a two parameter $O(2)$ symmetric problem in $\C^3$.