Anti-Control of Hopf Bifurcation for a Chaotic System with Infinite Equilibria

One method to change the bifurcation characteristics of chaotic systems is anti-control, which can either delay or advance bifurcation and transform an unstable state into a stable one. The chaotic system with infinite equilibria exhibits complex bifurcation characteristics. The Hopf bifurcation and hidden attractors with symmetric coexistence of the system are analyzed. An improved dynamic state feedback control method is adopted to reduce the tedious calculation process to prevent the Hopf bifurcation from being controlled. A hybrid controller that includes both nonlinear and linear controllers is set up for the system. With the method, the delay and stability of the Hopf bifurcation of the system are studied and the goal of anti-control is achieved. Numerical analysis verified the correctness.