一个新的三维混沌系统及其线性反馈同步

摘要

This paper reports a new three-dimensional continuous autonomous system,the system contains three parameters.The first two equations contain a nonlinear product term,and the third equation contains a cubic term.In this paper,the balance point stability of the new chaotic system,the power spectrum,the Lyapunov exponent and the dimension,and the Poincare cross section are analyzed.Moreover,the chaotic characteristics of the system are proved theoretically.Finally,the linear feedback synchronization control of the chaotic system is carried out,and the influence of the selection of the control parameters on the synchronization time is obtained.Through the theory and a mass of system emulation,the system,the ability of the system to produce chaos is proved,which provides a basis for further research on the application and optimization of chaotic systems in secure communication and information processing.%提出了一个含立方项的新三维连续自治混沌系统,该系统包含3个参数.其中前两个方程各含有一个非线性乘积项,第三个方程包含一个立方项.对新混沌系统的平衡点稳定性、功率谱、Lyapunov指数与维数、Poincare截面等的基本动力学特性进行分析,理论上证明了系统的混沌特性.最后进行混沌系统的线性反馈同步控制,得到控制参数的选取对同步时间的影响.因为系统的理论分析和数值仿真一致,从而证明了该系统产生混沌的能力,为进一步研究混沌系统在保密通信和信息处理等领域的应用与优化提供了理论基础.