中国物理B ›› 2023, Vol. 32 ›› Issue (8): 80503-080503.doi: 10.1088/1674-1056/acd68b

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Dynamical analysis, geometric control and digital hardware implementation of a complex-valued laser system with a locally active memristor

Yi-Qun Li(李逸群)1, Jian Liu(刘坚)1,†, Chun-Biao Li(李春彪)2,3, Zhi-Feng Hao(郝志峰)1, and Xiao-Tong Zhang(张晓彤)1   

  1. 1. School of Mathematical Sciences, University of Jinan, Jinan 250022, China;
    2. School of Artificial Intelligence, Nanjing University of Information Science and Technology, Nanjing 210044, China;
    3. Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science and Technology, Nanjing 210044, China
  • 收稿日期:2023-03-29 修回日期:2023-05-16 出版日期:2023-07-14 发布日期:2023-07-27
  • 通讯作者: Jian Liu E-mail:ss_liuj@ujn.edu.cn,liujian1990@163.com
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No.61773010) and Taishan Scholar Foundation of Shandong Province of China (Grant No.ts20190938).

Dynamical analysis, geometric control and digital hardware implementation of a complex-valued laser system with a locally active memristor

Yi-Qun Li(李逸群)1, Jian Liu(刘坚)1,†, Chun-Biao Li(李春彪)2,3, Zhi-Feng Hao(郝志峰)1, and Xiao-Tong Zhang(张晓彤)1   

  1. 1. School of Mathematical Sciences, University of Jinan, Jinan 250022, China;
    2. School of Artificial Intelligence, Nanjing University of Information Science and Technology, Nanjing 210044, China;
    3. Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science and Technology, Nanjing 210044, China
  • Received:2023-03-29 Revised:2023-05-16 Online:2023-07-14 Published:2023-07-27
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No.61773010) and Taishan Scholar Foundation of Shandong Province of China (Grant No.ts20190938).

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摘要： In order to make the peak and offset of the signal meet the requirements of artificial equipment, dynamical analysis and geometric control of the laser system have become indispensable. In this paper, a locally active memristor with non-volatile memory is introduced into a complex-valued Lorenz laser system. By using numerical measures, complex dynamical behaviors of the memristive laser system are uncovered. It appears the alternating appearance of quasi-periodic and chaotic oscillations. The mechanism of transformation from a quasi-periodic pattern to a chaotic one is revealed from the perspective of Hamilton energy. Interestingly, initial-values-oriented extreme multi-stability patterns are found, where the coexisting attractors have the same Lyapunov exponents. In addition, the introduction of a memristor greatly improves the complexity of the laser system. Moreover, to control the amplitude and offset of the chaotic signal, two kinds of geometric control methods including amplitude control and rotation control are designed. The results show that these two geometric control methods have revised the size and position of the chaotic signal without changing the chaotic dynamics. Finally, a digital hardware device is developed and the experiment outputs agree fairly well with those of the numerical simulations.

关键词: complex-valued chaotic systems, locally active memristor, multi-stability, Hamilton energy, geometric control

Abstract: In order to make the peak and offset of the signal meet the requirements of artificial equipment, dynamical analysis and geometric control of the laser system have become indispensable. In this paper, a locally active memristor with non-volatile memory is introduced into a complex-valued Lorenz laser system. By using numerical measures, complex dynamical behaviors of the memristive laser system are uncovered. It appears the alternating appearance of quasi-periodic and chaotic oscillations. The mechanism of transformation from a quasi-periodic pattern to a chaotic one is revealed from the perspective of Hamilton energy. Interestingly, initial-values-oriented extreme multi-stability patterns are found, where the coexisting attractors have the same Lyapunov exponents. In addition, the introduction of a memristor greatly improves the complexity of the laser system. Moreover, to control the amplitude and offset of the chaotic signal, two kinds of geometric control methods including amplitude control and rotation control are designed. The results show that these two geometric control methods have revised the size and position of the chaotic signal without changing the chaotic dynamics. Finally, a digital hardware device is developed and the experiment outputs agree fairly well with those of the numerical simulations.

Key words: complex-valued chaotic systems, locally active memristor, multi-stability, Hamilton energy, geometric control

中图分类号:  (Control of chaos, applications of chaos)

  • 05.45.Gg
05.45.Jn (High-dimensional chaos) 05.45.Pq (Numerical simulations of chaotic systems)