Abstract:The complicated behaviors of the model in 3D nonlinear switching system were investigated in details. Based on the local analysis, the critical conditions of Fold bifurcation and Hopf bifurcation were derived to explore the bifurcations of compound systems with different stable solutions of focus or stable cycle in the two subsystems. With the change of parameters, different types of nonsmooth bifurcations occurred in the switching system to result in chaotic oscillations. By Poincar mapping, the Lyapunov exponent of the switching system was calculated. Compared with bifurcation diagram, the effectiveness of the algorithm was verified. The results show that with Lyapunov index as criterion, the route to chaos via perioddoubling bifurcations in such compound system is revealed explicitly.