Bifurcation control analysis of a chaotic system

The Hopf bifurcation control of hyperchaotic system has become the focus of bifurcation researches. By setting up the controller for the hyperchaotic system, the critical point of Hopf bifurcation is delayed or advanced,and the stability of the system is changed. In this paper, based on the first Lyapunov coefficient, the Hopf bifurcation characteristics of a chaotic system are studied. The stability of the system is judged by the value of the first Lyapunov coefficient. The dynamic state feedback control method is used to set the nonlinear controller for the system. By adjusting the control parameters, the Hopf bifurcation of the system can be changed, and the unstable range becomes stable. Finally, by the numerical simulations observation, it is shown that the theoretical analysis is correct.