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Synchronization and Antisynchronization of Identical 4D Hyperchaotic Financial System with External Perturbation via Sliding Mode Control Technique

Author

Listed:
  • Fazal ur Rehman
  • Muhammad Rafiq Mufti
  • Muhammad Umar Farooq
  • Sami ud Din
  • Jawad Ali
  • Nadir Mehmood

Abstract

In this article, complete synchronization and antisynchronization in the identical financial chaotic system are presented. The proposed control strategies depend on first‐order sliding mode and adaptive integral sliding mode for complete synchronization and antisynchronization of the identical financial chaotic system. In the primary case, the system parameters should be known, and first‐order sliding mode control is utilized for synchronization and antisynchronization while in the second case, the system parameters are considered unknown. An adaptive integral sliding mode control strategy is utilized for synchronization and antisynchronization of the system considering the parameters unknown. The error system is changed into a particular structure containing a nominal part and several unknown terms to utilize the adaptive integral sliding mode control. Then, this error system is stabilized using integral sliding mode control. The stabilizing controller is usually developed based on the nominal part plus the compensator control part. To suppress the high‐frequency oscillation (chattering) phenomenon, smooth continuous compensator control can be used rather than conventional discontinuous control. The compensator controller along with the adapted law is derived such that the time derivative of the Lyapunov function becomes strictly negative. The effectiveness of the proposed method was tested through computer simulations. The proposed control strategies are verified for that Identical 4D hyperchaotic financial system to attain complete synchronization and antisynchronization along with the improved performance.

Suggested Citation

  • Fazal ur Rehman & Muhammad Rafiq Mufti & Muhammad Umar Farooq & Sami ud Din & Jawad Ali & Nadir Mehmood, 2022. "Synchronization and Antisynchronization of Identical 4D Hyperchaotic Financial System with External Perturbation via Sliding Mode Control Technique," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:4272138
    DOI: 10.1155/2022/4272138
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    References listed on IDEAS

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    1. Chen, Xiangyong & Park, Ju H. & Cao, Jinde & Qiu, Jianlong, 2017. "Sliding mode synchronization of multiple chaotic systems with uncertainties and disturbances," Applied Mathematics and Computation, Elsevier, vol. 308(C), pages 161-173.
    2. De Cesare, Luigi & Sportelli, Mario, 2005. "A dynamic IS-LM model with delayed taxation revenues," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 233-244.
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