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On the Synchronization and Stabilization of fractional-order chaotic systems: Recent advances and future perspectives

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  • Balootaki, Mohammad Ahmadi
  • Rahmani, Hossein
  • Moeinkhah, Hossein
  • Mohammadzadeh, Ardashir

Abstract

Chaos is one of the most significant findings in physics and engineering. Fractional-order chaotic systems are nonlinear systems with special features which, some of them include sensitivity to initial condition and the order of fractional derivative, unpredictable and complex dynamic behavior, high bandwidth and controllable noise-like behavior. By accepting this truth that any irregular behavior in a dynamic system is a sign of chaos and that a chaotic system is a deterministic system with pseudo-random behavior, chaos can be observed in different fields of science and engineering like mathematics, physics, mechanical, chemical and electrical engineering. Recently, control of fractional-order chaotic systems has been one of the most interesting topics that attracted many researchers’ idea. This paper deals with the comprehensive study of control and synchronization of fractional order chaotic systems, and shows how chaos is formed in developing inter-disciplinary researches of fractional order systems from the first research till today.

Suggested Citation

  • Balootaki, Mohammad Ahmadi & Rahmani, Hossein & Moeinkhah, Hossein & Mohammadzadeh, Ardashir, 2020. "On the Synchronization and Stabilization of fractional-order chaotic systems: Recent advances and future perspectives," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    • Handle: RePEc:eee:phsmap:v:551:y:2020:i:c:s0378437120300418
    DOI: 10.1016/j.physa.2020.124203
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    1. Zheng, Yi & Wu, Xiaoqun & Fan, Ziye & Wang, Wei, 2022. "Identifying topology and system parameters of fractional-order complex dynamical networks," Applied Mathematics and Computation, Elsevier, vol. 414(C).
    2. Dong, Youheng & Zhao, Geng, 2021. "A spatiotemporal chaotic system based on pseudo-random coupled map lattices and elementary cellular automata," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    3. Liu, Xianggang & Ma, Li, 2020. "Chaotic vibration, bifurcation, stabilization and synchronization control for fractional discrete-time systems," Applied Mathematics and Computation, Elsevier, vol. 385(C).

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