Infinite Period Bifurcation and Global Bifurcation Branches

Abstract

Branches of periodic solutions which exhibit the alternatives of the global Hopf bifurcation theorem are calculated for two general systems of differential equations. In the first, a branch of solutions is found which originates at a point of Hopf bifurcation and terminates with an infinite period bifurcation. In the second, there is a branch of periodic solutions connecting two Hopf bifurcation points, and a branch of doubly periodic solutions emanating from a periodic solution and terminating with an infinite period bifurcation.