Hopf bifurcation stabilization of Rössler System

This paper deals with the problem of Hopf bifurcation stabilization for Rössler system. Röseeler system has two cures of equilibria, and Hopf bifurcation may occur at some points of the equilibria. We present a method of controlling the Hopf bifurcation by state feedback. The method ensures that the equilibria of the uncontrolled Rössler system are not changed and that all equilibria of the closed loop system are asymptotically stable. The existing results only ensure that the equilibria in some neighborhood of the point of Hopf bifurcation are asymptotically stable.