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Carpet oscillator: A new megastable nonlinear oscillator with infinite islands of self-excited and hidden attractors

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Abstract

In this paper, we design a new two-dimensional nonlinear oscillator with infinite number of coexisting limit cycles distributed in a plane. One-third of these limit cycles are self-excited attractors while two-third of them are hidden attractors. Modifying this new system to its forced version, we obtain a new nonlinear system with infinite number of coexisting torus attractors and limit cycle attractors.

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Acknowledgements

This work is supported by ‘Engineering Technology Research Center of Population Health Informatization in Hebei Province’. One of the authors (TK) has been supported by the Polish National Science Centre, MAESTRO Programme – Project No. 2013 / 08 / A / ST8 / 00 / 780.

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Authors and Affiliations

  1. Department of Mathematics, College of Science, Hebei North University, Zhangjiakou, 075000, Hebei, China

    Yanxia Tang & Ye Tian

  2. Engineering Technology Research Center of Population Health Informatization in Hebei Province, Zhangjiakou, 075000, Hebei, China

    Yanxia Tang & Ye Tian

  3. Department of Electrical Engineering, Golpayegan University of Technology, Golpayegan, Iran

    Hamid Reza Abdolmohammadi

  4. Department of Mathematics, Faculty of Computer Science and Mathematics, University of Kufa, Najaf, Iraq

    Abdul Jalil M Khalaf

  5. Division of Dynamics, Lodz University of Technology, Stefanowskiego 1 / 15, 90-924 , Lodz, Poland

    Tomasz Kapitaniak

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  1. Yanxia Tang
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  2. Hamid Reza Abdolmohammadi
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  3. Abdul Jalil M Khalaf
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  4. Ye Tian
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  5. Tomasz Kapitaniak
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Corresponding author

Correspondence to Hamid Reza Abdolmohammadi.

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Tang, Y., Abdolmohammadi, H.R., Khalaf, A.J.M. et al. Carpet oscillator: A new megastable nonlinear oscillator with infinite islands of self-excited and hidden attractors. Pramana - J Phys 91, 11 (2018). https://doi.org/10.1007/s12043-018-1581-6

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  • DOI: https://doi.org/10.1007/s12043-018-1581-6

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