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.
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