Study of Universal Constants of Bifurcation in a Chaotic Sine Map

The symmetry breaking bifurcation of a sine map is discussed when the control parameter in the sine map is chosen as a bifurcation parameter. Based on the sine map, the bifurcation points can be derived by the iterative map. Then, the stability of the system is enhanced by employing a cubic and a linear chaotic controller to exactly control the locations of the bifurcation points. Moreover, the universal constants of the chaotic system have been obtained by numerical simulation. The validity of the theoretical analysis is proved by the diagrams of bifurcation and Lyapunov exponent.