具有多参数恒Lyapunov指数谱的新型统一混沌系统

万求真; 周昭腾

doi:10.11959/j.issn.1000-436x.2020080

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具有多参数恒Lyapunov指数谱的新型统一混沌系统

学术通信 | 更新时间：2024-06-05

- 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
- 通信学报 2020年41卷第6期页码：202-213
- 作者机构：
  
  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
- 作者简介：
  
  [ "万求真（1984- ），男，湖南岳阳人，博士，湖南师范大学副教授、硕士生导师，主要研究方向为模拟/射频集成电路设计、非线性系统与电路设计" ]
  [ "周昭腾（1993- ），男，湖南长沙人，湖南师范大学硕士生，主要研究方向为混沌电路与系统设计、忆阻器与忆阻系统" ]
- 基金信息：
  
  国家自然科学基金资助项目(61901169);湖南省自然科学基金资助项目(2019JJ40190);国家大学生创新创业训练计划基金资助项目(201910542049)
- DOI：10.11959/j.issn.1000-436x.2020080
  中图分类号： O231.2
- 网络首发：2020-06，
  
  纸质出版：2020-06-25
- 稿件说明：
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万求真, 周昭腾. 具有多参数恒Lyapunov指数谱的新型统一混沌系统[J]. 通信学报, 2020,41(6):202-213.

Qiuzhen WAN, Zhaoteng ZHOU. Novel unified chaotic system with multi-parameter invariable Lyapunov exponent spectrum[J]. Journal on Communications, 2020, 41(6): 202-213.
万求真, 周昭腾. 具有多参数恒Lyapunov指数谱的新型统一混沌系统[J]. 通信学报, 2020,41(6):202-213. DOI： 10.11959/j.issn.1000-436x.2020080.

Qiuzhen WAN, Zhaoteng ZHOU. Novel unified chaotic system with multi-parameter invariable Lyapunov exponent spectrum[J]. Journal on Communications, 2020, 41(6): 202-213. DOI： 10.11959/j.issn.1000-436x.2020080.

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。

Abstract

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.

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