Period doubling bifurcation control at 4 period point of discrete chaotic system

In this paper, taking one-dimensional quadratic discrete chaotic system as the research object, the nonlinear dynamic characteristics of the system such as period doubling bifurcation and chaos are studied. Using the state feedback control method, a nonlinear controller is set up to the system, and the period doubling bifurcation control is carried out at four period point of the system. By specifying the bifurcation parameter in advance, the control parameters value are inversely calculated. The four period bifurcation point appears at the prespecified location, and the purpose of period doubling bifurcation control is realized. The correctness of the theoretical analysis is verified by numerical simulation.