Abstract: In this paper, the five-dimensional hyperchaotic Pan system is studied. According to the high dimensional Hopf bifurcation theory and the Routh-Hurwitz theory, the stability of the non-zero equilibrium point of the system and the stability of the bifurcation solution are analyzed. The Hopf bifurcation and stability control of the system are set up by using the Washout control method. Through analyzing the controlled system, we obtain the corresponding relations between the bifurcation parameter and control parameters, and between the stability parameters and control parameters. These relationships show that by controlling the parameters of the controller, the bifurcation parameter and stability parameter of the system can be adjusted, and the Hopf bifurcation can be delayed and the stability range of the bifurcation solution can be changed. The numerical simulation proves the correctness of theoretical analyses.

Key words: Pan-like hyperchaos system, Hopf bifurcation, bifurcation control, Washout control law