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Graph-theoretic approach to synchronization of fractional-order coupled systems with time-varying delays via periodically intermittent control

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  • Xu, Yao
  • Li, Yanzhen
  • Li, Wenxue

Abstract

This paper deals with synchronization problem of fractional-order coupled systems (FOCSs) with time-varying delays via periodically intermittent control. Here, nonlinear coupling, time-varying internal delay and time-varying coupling delay are considered when modeling, which makes our model more general in comparison with the most existing fractional-order models. It is the first time that periodically intermittent control is applied to synchronizing FOCSs with time-varying delays. Combining Lyapunov method with graph-theoretic approach, some synchronization criteria are obtained. Moreover, the synchronization criteria we derive depend on the fractional order α, control gain, control rate and control period. Besides, the synchronization issues of fractional-order coupled chaotic systems with time-varying delays and fractional-order coupled Hindmarsh–Rose neuron systems with time-varying delays are also investigated as applications of our theoretical results, and relevant sufficient conditions are derived. Finally, numerical simulations with two examples are provided in order to demonstrate the effectiveness of the theoretical results and the feasibility of control strategy.

Suggested Citation

  • Xu, Yao & Li, Yanzhen & Li, Wenxue, 2019. "Graph-theoretic approach to synchronization of fractional-order coupled systems with time-varying delays via periodically intermittent control," Chaos, Solitons & Fractals, Elsevier, vol. 121(C), pages 108-118.
    • Handle: RePEc:eee:chsofr:v:121:y:2019:i:c:p:108-118
    DOI: 10.1016/j.chaos.2019.01.038
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    References listed on IDEAS

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    1. Shi, Lin & Yang, Huilan & Wang, Xin & Zhong, Shouming & Wang, Wenqin, 2018. "Synchronization of complex networks with asymmetric coupling via decomposing matrix method," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 180-185.
    2. Liang, Song & Wu, Ranchao & Chen, Liping, 2016. "Adaptive pinning synchronization in fractional-order uncertain complex dynamical networks with delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 49-62.
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    Cited by:

    1. He, Xinyi & Wang, Yuhan & Li, Xiaodi, 2021. "Uncertain impulsive control for leader-following synchronization of complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    2. Cai, Shuiming & Hou, Meiyuan, 2021. "Quasi-synchronization of fractional-order heterogeneous dynamical networks via aperiodic intermittent pinning control," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    3. Guo, Beibei & Xiao, Yu, 2023. "Intermittent synchronization for multi-link and multi-delayed large-scale systems with semi-Markov jump and its application of Chua’s circuits," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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