Bifurcation of the branching of a cycle in n-parameter family of dynamic systems with cosymmetry

A study is reported of the bifurcation of the branching of a cycle (Poincare-Andronov-Hopf bifurcation) from a smooth one-dimensional submanifold of equilibria of a dynamical system that depends on a vector parameter and admits cosymmetry. The paper reports a topological classification of local phase portraits near a known equilibrium, when the system parameter is close to its critical value that corresponds to an oscillatory instability. New phenomena that are not observed in the classical case of an isolated equilibrium include a delay of cycle creation with respect to the system parameter, loss of stability by the family of equilibria without loss of attraction, and the possibility of unstable supercritical self-oscillations. (c) 1997 American Institute of Physics.