CHAOS CONTROL AND HOPF BIFURCATION ANALYSIS OF A THREE-DIMENSIONAL CHAOTIC SYSTEM

In this paper, we study the effect of delayed feedback on the dynamics of a three-dimensional chaotic dynamical system and stabilize its chaotic behavior and control the respective unstable steady state. We derive an explicit formula in which a Hopf bifurcation occurs under some analytical conditions. Then the existence and stability of the Hopf bi-furcation are analyzed by considering the time delay τ as a bifurcation parameter. Furthermore, by numerical calculation and appropriate as-certaining of both the feedback strength K and time delay τ , we find certain threshold values of time delay at which an unstable equilibrium of the considered system is successfully controlled. Finally, we use nu-merical simulations to examine the derived analytical results and reveal more dynamical behaviors of the system.