  In this work we propose a feedback approach to regulate the chaotic behavior
of the whole family of the generalized Lorenz system, by designing a nonlinear
delayed feedback control. We first study the effect of the delay on the
dynamics of the system and we investigate the existence of Hopf bifurcations.
Then, by using the center manifold reduction technique and the normal form
theory, we derive the explicit formulas for the direction, stability and period
of the periodic solutions bifurcating from the steady state at certain critical
values of the delay.
