BIFURCATION ANALYSIS AND CHAOS CONTROL FOR LÜ SYSTEM WITH DELAYED FEEDBACK

Time-delayed feedback has been introduced as a powerful tool to control unstable periodic orbits or control unstable steady states. In the present paper, regarding the delay as a parameter, we investigate the effect of delay on the dynamics of Lü system with delayed feedback. After the effect of delay on the steady states is analyzed, Hopf bifurcation is studied, where the direction, stability and other properties of the bifurcating periodic solutions are determined by using the normal form theory and the center manifold theorem. Finally, we provide several numerical simulations, which indicate that when the delay passes through certain critical values, chaotic oscillation is converted into a stable steady state or a stable periodic orbit.