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Spectral Entropy Analysis and Synchronization of a Multi-Stable Fractional-Order Chaotic System using a Novel Neural Network-Based Chattering-Free Sliding Mode Technique

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  • Xiong, Pei-Ying
  • Jahanshahi, Hadi
  • Alcaraz, Raúl
  • Chu, Yu-Ming
  • Gómez-Aguilar, J.F.
  • Alsaadi, Fawaz E.

Abstract

An immense body of research has focused on chaotic systems, mainly because of their interesting applications in a wide variety of fields. A comprehensive understanding and synchronization of chaotic systems play pivotal roles in practical applications. To this end, the present study investigates a multi-stable fractional-order chaotic system. Firstly, some dynamical features of the system are described, and the chaotic behaviour of the system is verified. Then, both spectral entropy and spectral Min-Entropy are computed, and the phenomenon of multi-stability is shown. Besides, the combination of a new chattering-free robust sliding mode controller with a neural network observer is proposed for the synchronization of the fractional-order system. With the neural network estimator, unknown functions of the system are obtained, and the effects of disturbances are completely taken into account. Also, based on the Lyapunov stability theorem, the asymptotical stability of the closed-loop system is confirmed. Lastly, the proposed control technique is applied to the fractional-order system. Numerical results demonstrate the chattering-free and effective performance of the proposed control method for uncertain systems in the presence of unknown time-varying external disturbances.

Suggested Citation

  • Xiong, Pei-Ying & Jahanshahi, Hadi & Alcaraz, Raúl & Chu, Yu-Ming & Gómez-Aguilar, J.F. & Alsaadi, Fawaz E., 2021. "Spectral Entropy Analysis and Synchronization of a Multi-Stable Fractional-Order Chaotic System using a Novel Neural Network-Based Chattering-Free Sliding Mode Technique," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    • Handle: RePEc:eee:chsofr:v:144:y:2021:i:c:s096007792030967x
    DOI: 10.1016/j.chaos.2020.110576
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    1. Atangana, Abdon & Qureshi, Sania, 2019. "Modeling attractors of chaotic dynamical systems with fractal–fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 320-337.
    2. Jahanshahi, Hadi & Yousefpour, Amin & Wei, Zhouchao & Alcaraz, Raúl & Bekiros, Stelios, 2019. "A financial hyperchaotic system with coexisting attractors: Dynamic investigation, entropy analysis, control and synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 66-77.
    3. Chen, Shu-Bo & Jahanshahi, Hadi & Alhadji Abba, Oumate & Solís-Pérez, J.E. & Bekiros, Stelios & Gómez-Aguilar, J.F. & Yousefpour, Amin & Chu, Yu-Ming, 2020. "The effect of market confidence on a financial system from the perspective of fractional calculus: Numerical investigation and circuit realization," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    4. Ghanbari, Behzad & Atangana, Abdon, 2020. "A new application of fractional Atangana–Baleanu derivatives: Designing ABC-fractional masks in image processing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    5. Jahanshahi, Hadi & Yousefpour, Amin & Munoz-Pacheco, Jesus M. & Kacar, Sezgin & Pham, Viet-Thanh & Alsaadi, Fawaz E., 2020. "A new fractional-order hyperchaotic memristor oscillator: Dynamic analysis, robust adaptive synchronization, and its application to voice encryption," Applied Mathematics and Computation, Elsevier, vol. 383(C).
    6. Soradi-Zeid, Samaneh & Jahanshahi, Hadi & Yousefpour, Amin & Bekiros, Stelios, 2020. "King algorithm: A novel optimization approach based on variable-order fractional calculus with application in chaotic financial systems," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    7. Yousefpour, Amin & Jahanshahi, Hadi & Munoz-Pacheco, Jesus M. & Bekiros, Stelios & Wei, Zhouchao, 2020. "A fractional-order hyper-chaotic economic system with transient chaos," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    8. Wang, Shaojie & Bekiros, Stelios & Yousefpour, Amin & He, Shaobo & Castillo, Oscar & Jahanshahi, Hadi, 2020. "Synchronization of fractional time-delayed financial system using a novel type-2 fuzzy active control method," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
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