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Global Mittag-Leffler boundedness and synchronization for fractional-order chaotic systems

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  • Jian, Jigui
  • Wu, Kai
  • Wang, Baoxian

Abstract

This paper deals with the issues of the global Mittag-Leffler boundedness and synchronization for three-dimensional fractional order chaotic systems (FOCSs). First, by constructing proper generalized Lyapunov function and using the extremum principle of function, some new 3D ellipsoid estimations and a cylindrical domain estimation of the bounds are derived for the addressed fractional system without existence assumptions, which improve the earlier publications and can deduce some new estimations. Besides, linear feedback control strategies with a single state and one input or two inputs are proposed to achieve synchronization. Some new sufficient synchronization criteria are derived by inequality techniques. Comparison of our results with that of the existing ones shows that the computation of the bounds and the control gain constants is easier and simpler and the controllers here have more simple structures. Simulation results are given to show the validity of the proposed scheme.

Suggested Citation

  • Jian, Jigui & Wu, Kai & Wang, Baoxian, 2020. "Global Mittag-Leffler boundedness and synchronization for fractional-order chaotic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    • Handle: RePEc:eee:phsmap:v:540:y:2020:i:c:s0378437119317820
    DOI: 10.1016/j.physa.2019.123166
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    2. Bukhari, Ayaz Hussain & Raja, Muhammad Asif Zahoor & Rafiq, Naila & Shoaib, Muhammad & Kiani, Adiqa Kausar & Shu, Chi-Min, 2022. "Design of intelligent computing networks for nonlinear chaotic fractional Rossler system," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    3. Zhang, Hai & Cheng, Yuhong & Zhang, Hongmei & Zhang, Weiwei & Cao, Jinde, 2022. "Hybrid control design for Mittag-Leffler projective synchronization on FOQVNNs with multiple mixed delays and impulsive effects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 341-357.
    4. Peng, Qiu & Jian, Jigui, 2021. "Estimating the ultimate bounds and synchronization of fractional-order plasma chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).

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