Bifurcation analysis and chaos control of the modified Chua's circuit system

From the view of bifurcation and chaos control, the dynamics of modified Chua's circuit system are investigated by a delayed feedback method. Firstly, the local stability of the equilibria is discussed by analyzing the distribution of the roots of associated characteristic equation. The regions of linear stability of equilibria are given. It is found that there exist Hopf bifurcation and Hopf-zero bifurcation when the delay passes though a sequence of critical values. By using the normal form method and the center manifold theory, we derive the explicit formulas for determining the direction and stability of Hopf bifurcation. Finally, chaotic oscillation is converted into a stable equilibrium or a stable periodic orbit by designing appropriate feedback strength and delay. Some numerical simulations are carried out to support the analytic results.