Hopf’s Bifurcation Theorem and the Center Theorem of Liapunov

Abstract

In recent years numerous papers have dealt with the bifurcation of periodic orbits from an equilibrium point. The starting point for most investigations is the Liapunov Center Theorem [1] or the Hopf Bifurcation Theorem [1]. Local results concerning these theorems were published by Chafee [1], Henrard [1] Schmidt and Sweet [1] among many others, noted in previous sections, whereas Alexander and Yorke [1] discussed the global problem of the bifurcation of periodic orbits. They showed in their paper that Liapunov’s Center Theorem can be derived as a consequence of Hopf’s bifurcation theorem.