Bifurcation of Periodic Solutions from Steady Ones (Hopf Bifurcation) in Two Dimensions

Abstract

Up to now the only equilibrium solutions which have been introduced are steady ones. Now we shall show how a time-periodic solution may arise from bifurcation of a steady solution. In this case the symmetry of the forcing data, which is steady, is broken by the time-periodic solution. The dynamical system then has “a mind of its own” in the sense that the solution does not follow the symmetry imposed by the given data.