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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2022, Vol. 39 ›› Issue (5): 709-724.doi: 10.3969/j.issn.1005-3085.2022.05.003

• • 上一篇    下一篇

新混沌系统分析及其同步控制

时帅帅1,   刘立才2,   杜传红2   

  1. 1. 贵州工程应用技术学院信息工程学院，毕节  551700; 2. 安顺学院电子信息工程学院，安顺  561000
  • 出版日期:2022-10-15 发布日期:2022-12-15
  • 基金资助:
    贵州省教育厅自然科学青年成长研究项目(KY[2019]160).

Analysis of a New Chaotic System and Its Synchronization Control

SHI Shuaishuai1,   LIU Licai2,   DU Chuanhong2   

  1. 1. School of Information Engineering, Guizhou University of Engineering Science, Bijie 551700;
    2. School of Electronic and Information Engineering, Anshun University, Anshun 561000
  • Online:2022-10-15 Published:2022-12-15
  • Supported by:
    The Project of Young Scientific and Technological Talents for Colleges and Universities in Guizhou Province (KY[2019]160).

PDF (PC)

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摘要：

提出了一个新混沌系统，通过Matlab对该系统进行了分岔图、Lyapunov指数、相图等仿真分析，证实了在选定特定参数下，该系统为混沌系统。随着参数的改变，该系统会出现周期--倍周期--混沌--周期--倍周期--混沌交替现象，具有较复杂的动力学特性及对初值的敏感性，通过Multisim电路仿真证实了该系统的物理可实现性。针对提出的新混沌系统，设计了错位投影同步控制器，从理论上证实了在同步控制器的作用下该系统与Chen混沌系统达到了同步，通过Matlab仿真证实了同步控制器的有效性。最后，在同步控制器作用下实现了新混沌系统和Chen混沌系统的数字加密传输。

关键词: 混沌系统, 动态分析, 同步控制, 电路仿真, 加密传输

Abstract:

In this paper, a new chaotic system is proposed. Through the analysis of the bifurcation diagram, Lyapunov exponent and phase diagram of the system, it is proved that the system is a chaotic system under certain parameters. When the parameters are changed, the system exhibits the alternation behavior of period--doubling period--chaos--period--doubling period--chaos, which indicates that the system has more complex dynamic characteristics and sensitivity to the initial value. In addition, the Multisim circuit simulation software is applied to verify the physical realizability of the system. Moreover, based on the new chaotic system, a mismatch projection synchronization controller is designed, which theoretically confirms that the system is synchronized with the Chen chaotic system under the action of the controller, the effectiveness of the synchronous controller is validated by Matlab simulation. Finally, the digital encrypted transmission is realized under the action of the synchronous controller.

Key words: Chaotic system, dynamic analysis, synchronous control, circuit simulation, encrypted transmission

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