中国物理B ›› 2021, Vol. 30 ›› Issue (11): 110502-110502.doi: 10.1088/1674-1056/abf4fb

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A memristive map with coexisting chaos and hyperchaos

Sixiao Kong(孔思晓)1,2, Chunbiao Li(李春彪)1,2,†, Shaobo He(贺少波)3, Serdar Çiçek4, and Qiang Lai(赖强)5   

  1. 1 Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology(CICAEET), Nanjing University of Information Science & Technology, Nanjing 210044, China;
    2 School of Artificial Intelligence, Nanjing University of Information Science & Technology, Nanjing 210044, China;
    3 School of Physics and Electronics, Central South University, Changsha 410083, China;
    4 Department of Electronic & Automation, Vocational School of Hacıbektaş, Nevşehir Hacı Bektaş Veli University, Hacıbektaş 50800, Nevşehir, Turkey;
    5 School of Electrical and Automation Engineering, East China Jiaotong University, Nanchang 330013, China
  • 收稿日期:2021-02-03 修回日期:2021-03-17 接受日期:2021-04-06 出版日期:2021-10-13 发布日期:2021-10-13
  • 通讯作者: Chunbiao Li E-mail:goontry@126.com,chunbiaolee@nuist.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 61871230), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20181410), and the Postgraduate Research and Practice Innovation Project of Jiangsu Province, China (Grant No. SJCX21_0350).

A memristive map with coexisting chaos and hyperchaos

Sixiao Kong(孔思晓)1,2, Chunbiao Li(李春彪)1,2,†, Shaobo He(贺少波)3, Serdar Çiçek4, and Qiang Lai(赖强)5   

  1. 1 Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology(CICAEET), Nanjing University of Information Science & Technology, Nanjing 210044, China;
    2 School of Artificial Intelligence, Nanjing University of Information Science & Technology, Nanjing 210044, China;
    3 School of Physics and Electronics, Central South University, Changsha 410083, China;
    4 Department of Electronic & Automation, Vocational School of Hacıbektaş, Nevşehir Hacı Bektaş Veli University, Hacıbektaş 50800, Nevşehir, Turkey;
    5 School of Electrical and Automation Engineering, East China Jiaotong University, Nanchang 330013, China
  • Received:2021-02-03 Revised:2021-03-17 Accepted:2021-04-06 Online:2021-10-13 Published:2021-10-13
  • Contact: Chunbiao Li E-mail:goontry@126.com,chunbiaolee@nuist.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 61871230), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20181410), and the Postgraduate Research and Practice Innovation Project of Jiangsu Province, China (Grant No. SJCX21_0350).

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摘要： By introducing a discrete memristor and periodic sinusoidal functions, a two-dimensional map with coexisting chaos and hyperchaos is constructed. Various coexisting chaotic and hyperchaotic attractors under different Lyapunov exponents are firstly found in this discrete map, along with which other regimes of coexistence such as coexisting chaos, quasi-periodic oscillation, and discrete periodic points are also captured. The hyperchaotic attractors can be flexibly controlled to be unipolar or bipolar by newly embedded constants meanwhile the amplitude can also be controlled in combination with those coexisting attractors. Based on the nonlinear auto-regressive model with exogenous inputs (NARX) for neural network, the dynamics of the memristive map is well predicted, which provides a potential passage in artificial intelligence-based applications.

关键词: memristor, hyperchaos, coexisting attractors, amplitude control, neural network

Abstract: By introducing a discrete memristor and periodic sinusoidal functions, a two-dimensional map with coexisting chaos and hyperchaos is constructed. Various coexisting chaotic and hyperchaotic attractors under different Lyapunov exponents are firstly found in this discrete map, along with which other regimes of coexistence such as coexisting chaos, quasi-periodic oscillation, and discrete periodic points are also captured. The hyperchaotic attractors can be flexibly controlled to be unipolar or bipolar by newly embedded constants meanwhile the amplitude can also be controlled in combination with those coexisting attractors. Based on the nonlinear auto-regressive model with exogenous inputs (NARX) for neural network, the dynamics of the memristive map is well predicted, which provides a potential passage in artificial intelligence-based applications.

Key words: memristor, hyperchaos, coexisting attractors, amplitude control, neural network

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a
05.45.Ac (Low-dimensional chaos) 05.45.Pq (Numerical simulations of chaotic systems) 05.45.Gg (Control of chaos, applications of chaos)