具有多参数恒Lyapunov指数谱的新型统一混沌系统  

Novel unified chaotic system with multi-parameter invariable Lyapunov exponent spectrum

作　　者：万求真 周昭腾 WAN Qiuzhen;ZHOU Zhaoteng(College of Information Science and Engineering,Hunan Normal University,Changsha 410081,China;Provincial Key Laboratory of Intelligent Computing and Language Information Processing,Changsha 410081,China)

机构地区：[1]湖南师范大学信息科学与工程学院,湖南长沙410081 [2]智能计算与语言信息处理湖南省重点实验室,湖南长沙410081

出　　处：《通信学报》2020年第6期202-213,共12页Journal on Communications

基　　金：国家自然科学基金资助项目(No.61901169);湖南省自然科学基金资助项目(No.2019JJ40190);国家大学生创新创业训练计划基金资助项目(No.201910542049)。

摘　　要：基于传统的Qi混沌系统,通过增加控制参数和改变非线性项相结合的方法构造了一种具有复杂混沌特性的新型统一混沌系统。首先,分析了所提系统的动力学行为,数值仿真了相图、时域波形图、Poincare截面图和功率谱图;其次,讨论了系统参数变化时Lyapunov指数谱、分岔图和混沌信号幅度对整个系统的影响,分析表明,所提统一混沌系统能产生4种新的具有多参数恒Lyapunov指数谱特性的双翼混沌吸引子,并存在多种全局和局部的非线性调幅参数;再次,以所提系统的第一种混沌吸引子为例,引入2种新的非线性函数,实现了网格多翼的扩展;最后,搭建所提统一混沌系统的硬件电路,实验观察到4种新混沌吸引子,与数值仿真结果一致,验证了所提系统的可行性。Based on the traditional Qi chaotic system,a novel unified chaotic system with the complex chaotic characteristics was constructed by adding the control parameters and modifying the nonlinear terms.Firstly,basic dynamical characteristics of chaotic system were analyzed,and phase portrait,time domain waveform diagram,Poincare mapping and power spectrum diagram were numerically simulated.Secondly,system parameters influence on chaotic system was discussed through Lyapunov exponent spectrum,bifurcation diagrams and chaotic signal amplitude.It was found that the unified chaotic system can generate the four new types of two-wing chaotic attractors with the multi-parameter invariable Lyapunov exponent spectrum characteristics.Meanwhile,there exist the functions of the global and local nonlinear amplitude modulation parameters.Thirdly,taking the first chaotic attractor of system as an example by introducing the two new types of nonlinear functions,the expansion of grid multi-wing attractor was realized.Finally,the hardware circuit of novel unified chaotic system was constructed.The four new types of chaotic attractors are observed experimentally,which is consistent with numerical simulation results and verified the feasibility of the proposed system.

关 键 词：统一混沌系统 恒Lyapunov指数谱 混沌吸引子 

分 类 号：O231.2[理学—运筹学与控制论]