Delayed feedback control of time-delayed chaotic systems: Analytical approach at Hopf bifurcation

This Letter is concerned with bifurcation and chaos control in scalar delayed differential equations with delay parameter τ. By linear stability analysis, the conditions under which a sequence of Hopf bifurcation occurs at the equilibrium points are obtained. The delayed feedback controller is used to stabilize unstable periodic orbits. To find the controller delay, it is chosen such that the Hopf bifurcation remains unchanged. Also, the controller feedback gain is determined such that the corresponding unstable periodic orbit becomes stable. Numerical simulations are used to verify the analytical results.