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Adaptive synchronization of fractional-order complex networks involving non-differentiable time-varying delays

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  • Wang, Wenbo
  • Du, Feifei

Abstract

In this paper, the synchronization problem of fractional-order complex networks (FOCNs) involving non-differentiable time-varying delays is investigated and two novel adaptive control strategies are proposed. The boundedness of fractional-order adaptive controller gains, while crucial for engineering applications, presents unresolved challenges owing to the non-locality inherent in fractional-order calculus. To address this challenge, a synchronization criterion for centralized adaptive control of FOCNs involving non-differentiable time-varying delays is established by employing the fractional-order Halanay inequality. Moreover, the boundedness of the controller gains is proved via the property of the Mittag-Leffler function. Furthermore, by utilizing the Riemann Liouville integral property of function and the fractional-order Halanay inequality with a perturbation function, a synchronization criterion for decentralized adaptive control of FOCNs involving non-differentiable time-varying delays is developed. Finally, numerical examples are provided to demonstrate the effectiveness of the theoretical results.

Suggested Citation

  • Wang, Wenbo & Du, Feifei, 2026. "Adaptive synchronization of fractional-order complex networks involving non-differentiable time-varying delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 240(C), pages 226-237.
    • Handle: RePEc:eee:matcom:v:240:y:2026:i:c:p:226-237
    DOI: 10.1016/j.matcom.2025.07.015
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    1. Zhou, Jin & Lu, Jun-an, 2007. "Topology identification of weighted complex dynamical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 481-491.
    2. Chai, Yi & Chen, Liping & Wu, Ranchao & Sun, Jian, 2012. "Adaptive pinning synchronization in fractional-order complex dynamical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5746-5758.
    3. Wang, Kangsheng & Wen, Fenghua & Gong, Xu, 2024. "Oil prices and systemic financial risk: A complex network analysis," Energy, Elsevier, vol. 293(C).
    4. Hu, Jingting & Sui, Guixia & Li, Xiaodi, 2020. "Fixed-time synchronization of complex networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    5. 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.
    6. Chen Huang & Xinbiao Lu & Jun Zhou & Buzhi Qin, 2020. "The optimal synchronizability of complex networks with saturated coupling strength," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 31(10), pages 1-12, October.
    7. Yang, Dongsheng & Yu, Yongguang & Wang, Hu & Ren, Guojian & Zhang, Xiaoli, 2024. "Successive lag synchronization of heterogeneous distributed-order coupled neural networks with unbounded delayed coupling," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    8. Li, Xuemei & Liu, Xinge & Wang, Fengxian, 2023. "Anti-synchronization of fractional-order complex-valued neural networks with a leakage delay and time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    9. 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.
    10. Du, Feifei & Lu, Jun-Guo & Zhang, Qing-Hao, 2025. "Estimating the region of attraction on fractional-order complex networks with time-varying delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 234(C), pages 438-458.
    11. Yang, Juanping & Sheng, Yuhong & Li, Hong-Li & Hu, Cheng, 2023. "Stability and adaptive control-based synchronization of delayed uncertain fractional-order gene regulatory networks," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
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