Hopf bifurcation analysis of the generalized Lorenz system with time delayed feedback control

摘要

In this work we propose a feedback approach to regulate the chaotic behaviorof the whole family of the generalized Lorenz system, by designing a nonlineardelayed feedback control. We first study the effect of the delay on thedynamics of the system and we investigate the existence of Hopf bifurcations.Then, by using the center manifold reduction technique and the normal formtheory, we derive the explicit formulas for the direction, stability and periodof the periodic solutions bifurcating from the steady state at certain criticalvalues of the delay.