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Chin. Phys. B, 2021, Vol. 30(11): 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 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
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.
Keywords:  memristor      hyperchaos      coexisting attractors      amplitude control      neural network  
Received:  03 February 2021      Revised:  17 March 2021      Accepted manuscript online:  06 April 2021
PACS:  05.45.-a (Nonlinear dynamics and chaos)  
  05.45.Ac (Low-dimensional chaos)  
  05.45.Pq (Numerical simulations of chaotic systems)  
  05.45.Gg (Control of chaos, applications of chaos)  
Fund: 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).
Corresponding Authors:  Chunbiao Li     E-mail:,

Cite this article: 

Sixiao Kong(孔思晓), Chunbiao Li(李春彪), Shaobo He(贺少波), Serdar Çiçek, and Qiang Lai(赖强) A memristive map with coexisting chaos and hyperchaos 2021 Chin. Phys. B 30 110502

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