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Cluster Synchronization in Variable-Order Fractional Community Network via Intermittent Control

Author

Listed:
  • Yi Wang

    (School of Mathematics and Statistic, Jiangxi Normal University, Nanchang 330022, China)

  • Zhaoyan Wu

    (School of Mathematics and Statistic, Jiangxi Normal University, Nanchang 330022, China)

Abstract

In this paper, the cluster synchronization of a variable-order fractional community network with nonidentical dynamics is investigated. For achieving the cluster synchronization, intermittent controllers are designed, and the sufficient conditions with respect to system parameters, intermittent control instants and control gains are derived based on stability theory of fractional-order system and linear matrix inequalities (LMIs). To avoid verifying the LMIs, a corresponding simple corollary is provided. Finally, a numerical example is performed to verify the derived result.

Suggested Citation

  • Yi Wang & Zhaoyan Wu, 2021. "Cluster Synchronization in Variable-Order Fractional Community Network via Intermittent Control," Mathematics, MDPI, vol. 9(20), pages 1-12, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:20:p:2596-:d:657413
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    References listed on IDEAS

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    1. Dehestani, H. & Ordokhani, Y. & Razzaghi, M., 2020. "Application of fractional Gegenbauer functions in variable-order fractional delay-type equations with non-singular kernel derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    2. Lu, Jun Guo & Chen, Guanrong, 2006. "A note on the fractional-order Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 685-688.
    3. Zhou, Jiaying & Zhao, Yi & Wu, ZhaoYan, 2019. "Cluster synchronization of fractional-order directed networks via intermittent pinning control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 519(C), pages 22-33.
    4. Kachia, Krunal & Solís-Pérez, J.E. & Gómez-Aguilar, J.F., 2020. "Chaos in a three-cell population cancer model with variable-order fractional derivative with power, exponential and Mittag-Leffler memories," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    5. Xu, Liguang & Chu, Xiaoyan & Hu, Hongxiao, 2021. "Quasi-synchronization analysis for fractional-order delayed complex dynamical networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 594-613.
    6. Ghanbari, Behzad & Gómez-Aguilar, J.F., 2018. "Modeling the dynamics of nutrient–phytoplankton–zooplankton system with variable-order fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 114-120.
    7. Wu, Fei & Gao, Renbo & Liu, Jie & Li, Cunbao, 2020. "New fractional variable-order creep model with short memory," Applied Mathematics and Computation, Elsevier, vol. 380(C).
    8. Ding, Dawei & Yan, Jie & Wang, Nian & Liang, Dong, 2017. "Pinning synchronization of fractional order complex-variable dynamical networks with time-varying coupling," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 41-50.
    9. Xiaoli Gong & Luyining Gan & Zhaoyan Wu, 2016. "Adaptive impulsive cluster synchronization in community network with nonidentical nodes," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 27(01), pages 1-15, January.
    10. Feng, Jianwen & Yang, Pan & Zhao, Yi, 2016. "Cluster synchronization for nonlinearly time-varying delayed coupling complex networks with stochastic perturbation via periodically intermittent pinning control," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 52-68.
    11. Wang, Fei & Yang, Yongqing, 2018. "Intermittent synchronization of fractional order coupled nonlinear systems based on a new differential inequality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 142-152.
    12. Liu, Lingfeng & Liu, Kui & Xiang, Hongyue & Liu, Qian, 2020. "Pinning impulsive cluster synchronization of complex dynamical network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
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