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Dynamics analysis and fractional-order nonlinearity system via memristor-based Chua oscillator

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Abstract

This article discusses the utilisation of a Chua oscillator with a memristor to produce chaos with minimal nonlinearity. The memristor, a device that changes its flux or charges over time, has its nonlinear strength altered fractionally to determine the lowest-order memristor nonlinearity for generating chaos. An experimental analog circuit in real-time has been constructed. A linear parameter varying (LPV) approach, incorporating a suitable Lyapunov functional (LK) method, has been introduced to find new sufficient conditions for the robust stability of the resulting closed-loop system through linear matrix inequalities (LMIs). By observing the behaviour of the system without control, it is possible to understand the basic characteristics of chaotic oscillations and how they are affected by changes in the fractional order. These results can then be used as a starting point to study the effectiveness of various control techniques, such as feedback control, in reducing chaos and stabilising the system of this article. The efficiency of the cost-function-based control scheme is evaluated using the simulation results and relevant applications are addressed.

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Acknowledgements

SS and VP acknowledges the Basic Research Program of the National Research University, Higher School of Economics, Moscow. RV acknowledges the Thailand Science Research and Innovation (TSRI) Grant Fund No. 64A146000001.

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Authors and Affiliations

  1. Laboratory of Complex Systems Modelling and Control, Faculty of Computer Science, National Research University, HSE Moscow, Russia

    S Sabarathinam & Viktor Papov

  2. Beijing Key Laboratory of Computational Intelligence and Intelligent System, Beijing University of Technology, Beijing, 100124, China

    Zi-Peng Wang

  3. Beijing Institute of Artificial Intelligence, Beijing University of Technology, Beijing, 100124, China

    Zi-Peng Wang

  4. Beijing Laboratory of Smart Environmental Protection, Beijing University of Technology, Beijing, 100124, China

    Zi-Peng Wang

  5. Department of Mathematics, Faculty of Science and Technology, Phuket Rajabhat University, Phuket, 83000, Thailand

    R Vadivel

  6. Computational Intelligence Laboratory, Toyota Technological Institute, Nagoya, 468-8511, Japan

    NALLAPPAN Gunasekaran

  7. Eastern Michigan Joint College of Engineering, Beibu Gulf University, Qinzhou, 535011, China

    NALLAPPAN Gunasekaran

Authors
  1. S Sabarathinam
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  2. Viktor Papov
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  3. Zi-Peng Wang
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  4. R Vadivel
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  5. NALLAPPAN Gunasekaran
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Corresponding author

Correspondence to NALLAPPAN Gunasekaran.

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Sabarathinam, S., Papov, V., Wang, ZP. et al. Dynamics analysis and fractional-order nonlinearity system via memristor-based Chua oscillator. Pramana - J Phys 97, 107 (2023). https://doi.org/10.1007/s12043-023-02590-5

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  • DOI: https://doi.org/10.1007/s12043-023-02590-5

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