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Chaotic vibration, bifurcation, stabilization and synchronization control for fractional discrete-time systems

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  • Liu, Xianggang
  • Ma, Li

Abstract

The main intention of this paper is to investigate the dynamics of fractional Cubic map and fractional Holmes map from four perspectives: chaos, bifurcation, stabilization and synchronization. Via Jacobian matrix algorithm, we estimate the largest Lyapunov exponents of fractional maps to examine the existence of chaos in accordance with the observation of chaotic vibration affected by fractional difference order. In addition, with the help of the novel asymptotic stability criterion for linear incommensurate fractional difference systems, the effective control laws of stabilization and synchronization for fractional chaotic maps are achieved, respectively. Besides, experimental investigations and numerical simulations are implemented to further verify the effectiveness of the proposed results.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:385:y:2020:i:c:s0096300320303842
    DOI: 10.1016/j.amc.2020.125423
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    1. Zhao, Mingfang & Li, Hong-Li & Zhang, Long & Hu, Cheng & Jiang, Haijun, 2023. "Quasi-synchronization of discrete-time fractional-order quaternion-valued memristive neural networks with time delays and uncertain parameters," Applied Mathematics and Computation, Elsevier, vol. 453(C).
    2. Silva-Juárez, Alejandro & Tlelo-Cuautle, Esteban & de la Fraga, Luis Gerardo & Li, Rui, 2021. "Optimization of the Kaplan-Yorke dimension in fractional-order chaotic oscillators by metaheuristics," Applied Mathematics and Computation, Elsevier, vol. 394(C).

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