一种限定混沌状态变量运动区域的方法  

A method of limiting motion area of chaotic state variables

作　　者：赵柏山[1] 刘晓晓[1] 张学松[1] ZHAO Bai-shan;LIU Xiao-xiao;ZHANG Xue-song(School of Information Science and Engineering,Shenyang University of Technology,Shenyang 110870,China)

机构地区：[1]沈阳工业大学信息科学与工程学院,沈阳110870

出　　处：《沈阳工业大学学报》2019年第1期62-67,共6页Journal of Shenyang University of Technology

基　　金：辽宁省教育厅一般科研项目(L2014053)

摘　　要：为了获得特定频谱覆盖范围的混沌信号,采用将相空间运动轨迹限定在一定区域的方法,在Lü混沌系统基础上增加非线性约束项,构成新的三维自治混沌系统,并对系统的基本动力学特性进行了理论分析和数值仿真.利用Poincaré截面法和Lyapunov指数法验证了新系统为混沌系统,分析了非线性项中参数a对系统相空间运动轨迹的影响,并找出了极限环运动状态和混沌运动状态之间存在的过渡点.结果表明,增加非线性项可以将系统的状态变量限定在一个圆环内运动,从而获得目标信号,并验证了该方法的可行性.In order to obtain the chaotic signal with the specific spectrum coverage,a method of limiting the phase space motion trajectories in a certain area was adopted. Based on the Lü chaotic system,a new three-dimensional autonomous chaotic system was constituted through increasing the nonlinear constraint term. The theoretical analysis and numerical simulation were performed for the basic dynamic characteristics of the system. The newsystem was proved to be a chaotic system through the Poincaré section and Lyapunov exponent methods,the effect of parameter a in the nonlinear term on the phase space motion trajectories was analyzed,and the transition point between the limit cycle motion state and chaotic motion state was found out. The results show that through increasing the nonlinear term,the state variables of the system can be limited to the motion in a circular loop to obtain the target signal,which verifies the feasibility of the proposed method.

关 键 词：混沌系统 Lü混沌系统 状态变量 非线性项 运动区域 相轨迹 参数 功率谱 

分 类 号：TN918[电子电信—通信与信息系统]