强迫布鲁塞尔振子动力学行为和全局指数同步的数值仿真

摘要

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.%用Matlab软件数值模拟了系统分歧和混沌等的动力学行为发生的全过程,基于最大Lyapunov指数谱、分岔图、庞加莱截面以及功率谱和返回映射等仿真结果揭示了此系统混沌行为的普适特征.采用线性反馈同步控制方法实现该系统的全局指数同步.用Lyapunov第二方法从理论上证明了该同步方法的有效性.同时对同步系统进行仿真,验证了方法的有效性.