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Quasi-synchronization of heterogenous fractional-order dynamical networks with time-varying delay via distributed impulsive control

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  • Wang, Fei
  • Zheng, Zhaowen
  • Yang, Yongqing

Abstract

This paper investigates the quasi-synchronization problem of a heterogeneous dynamical network. All nodes have fractional order dynamical behavior with time-varying delay. The distributed impulsive control strategy is applied to drive all the nodes to approximately synchronize with the target orbit within a nonzero error bound. A new comparison principle of impulsive fractional order functional differential equation has been built at first. Then, based on the Lyapunov stability theory, some basic theories of fractional order functional differential equation, and the definition of an average impulsive interval, some quasi-synchronization criteria are derived with explicit expressions of the error bound. Both synchronizing impulses and desynchronizing impulses are discussed in this paper. Finally, two numerical examples are presented to illustrate the validity of the theoretical analysis.

Suggested Citation

  • Wang, Fei & Zheng, Zhaowen & Yang, Yongqing, 2021. "Quasi-synchronization of heterogenous fractional-order dynamical networks with time-varying delay via distributed impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    • Handle: RePEc:eee:chsofr:v:142:y:2021:i:c:s0960077920308572
    DOI: 10.1016/j.chaos.2020.110465
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    References listed on IDEAS

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    1. Chen, Boshan & Chen, Jiejie, 2015. "Razumikhin-type stability theorems for functional fractional-order differential systems and applications," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 63-69.
    2. Wang, Fei & Yang, Yongqing, 2018. "Quasi-synchronization for fractional-order delayed dynamical networks with heterogeneous nodes," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 1-14.
    3. Yang, Huilan & Wang, Xin & Zhong, Shouming & Shu, Lan, 2018. "Synchronization of nonlinear complex dynamical systems via delayed impulsive distributed control," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 75-85.
    4. Li, Hong-Li & Hu, Cheng & Jiang, Yao-Lin & Wang, Zuolei & Teng, Zhidong, 2016. "Pinning adaptive and impulsive synchronization of fractional-order complex dynamical networks," Chaos, Solitons & Fractals, Elsevier, vol. 92(C), pages 142-149.
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    Citations

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    Cited by:

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    2. Peng, Qiu & Jian, Jigui, 2023. "Asymptotic synchronization of second-fractional -order fuzzy neural networks with impulsive effects," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    3. Yong Tang & Lang Zhou & Jiahui Tang & Yue Rao & Hongguang Fan & Jihong Zhu, 2023. "Hybrid Impulsive Pinning Control for Mean Square Synchronization of Uncertain Multi-Link Complex Networks with Stochastic Characteristics and Hybrid Delays," Mathematics, MDPI, vol. 11(7), pages 1-18, April.
    4. Fan, Hongguang & Shi, Kaibo & Zhao, Yi, 2022. "Global μ-synchronization for nonlinear complex networks with unbounded multiple time delays and uncertainties via impulsive control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).
    5. 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.
    6. Du, Feifei & Lu, Jun-Guo, 2021. "New approach to finite-time stability for fractional-order BAM neural networks with discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).

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