Symmetry breaking bifurcation analysis and control of a cubic discrete chaotic system

The period-doubling bifurcation physical process of a cubic discrete chaotic systems is obtained by studying the bifurcation characteristics of the system. Existence of the symmetry breaking bifurcation is looked into by selecting the bifurcation parameter. The cause of symmetry breaking bifurcation is investigated by solving the two-period bifurcation solutions of the system, and the critical value of symmetry breaking bifurcation recovery is got. With using the state feedback control method, a nonlinear controller is proposed to control the bifurcation of the system, and the influence of the controller with different control parameters on the bifurcation characteristics of the system is analyzed. By adjusting the control parameters of the controller, the position of bifurcation point is changed. Then, the delay or advance of period-doubling bifurcation and the appearance of symmetry breaking bifurcation are carried out. The purpose of bifurcation control is realized.