Determining the controllable conditions for time-delayed feedback chaos control

Abstract

Based on Hopf bifurcation theory and methods in time-delayed systems, we ana lytically determine some general conditions of time-delayed feedback control of three-dimensional autonomous chaotic systems. With this method, a criterion for the stability of periodic solution under control and for the direction of Hopf b ifurcation is derived theoretically studied. Applying the method to the control of some three-dimensional autonomous chaotic systems, we can analytically find the cont rollable parameter in this region. Choosing parameters in it, we can successfull y stabilize chaotic orbits to periodic states.