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Chin. Phys. B, 2018, Vol. 27(4): 040502    DOI: 10.1088/1674-1056/27/4/040502
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A new nonlinear oscillator with infinite number of coexisting hidden and self-excited attractors

Yan-Xia Tang(唐妍霞)1,2, Abdul Jalil M Khalaf3, Karthikeyan Rajagopal4,5, Viet-Thanh Pham6, Sajad Jafari7, Ye Tian(田野)1,2
1. College of Science, Hebei North University, Zhangjiakou 075000, China;
2. Engineering Technology Research Center of Population Health Informatization in Hebei Province, Zhangjiakou 075000, China;
3. Department of Mathematics, Faculty of Computer Science and Mathematics, University of Kufa, Najaf, Iraq;
4. Department of Electrical and Communication Engineering, the PNG University of Technology, Lae;
5. Centre for Nonlinear Dynamics, Defense University, Ethiopia;
6. Modeling Evolutionary Algorithms Simulation and Artificial Intelligence, Faculty of Electrical & Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam;
7. Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875-4413, Iran
Abstract  

In this paper, we introduce a new two-dimensional nonlinear oscillator with an infinite number of coexisting limit cycles. These limit cycles form a layer-by-layer structure which is very unusual. Forty percent of these limit cycles are self-excited attractors while sixty percent of them are hidden attractors. Changing this new system to its forced version, we introduce a new chaotic system with an infinite number of coexisting strange attractors. We implement this system through field programmable gate arrays.

Keywords:  chaotic oscillators      multistability      hidden attractors  
Received:  09 September 2017      Revised:  07 December 2017      Accepted manuscript online: 
PACS:  05.45.-a (Nonlinear dynamics and chaos)  
  05.45.Ac (Low-dimensional chaos)  
  05.45.Pq (Numerical simulations of chaotic systems)  
Corresponding Authors:  Viet-Thanh Pham     E-mail:  phamvietthanh@tdt.edu.vn

Cite this article: 

Yan-Xia Tang(唐妍霞), Abdul Jalil M Khalaf, Karthikeyan Rajagopal, Viet-Thanh Pham, Sajad Jafari, Ye Tian(田野) A new nonlinear oscillator with infinite number of coexisting hidden and self-excited attractors 2018 Chin. Phys. B 27 040502

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