The software of Matlab is used in this paper to simulate the whole process of dynamic behavior for the system divergence and chaos. The simulation results, such as the maximum Lyapunov exponent spectrum and bifurcation diagram, Poincare cross section, power spectrum and return map, are described to investigate the characteristics of system chaotic behavior. Meanwhile, the globally exponentially synchronization of the chaotic system is achieved by linear feedback synchronization control. The validity of the synchronous method is then theoretically performed by Lyapunov second method. Moreover, the simulation of synchronous system also verifies the effectiveness of the synchronous method.