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Estimating the region of attraction on fractional-order complex networks with time-varying delay

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  • Du, Feifei
  • Lu, Jun-Guo
  • Zhang, Qing-Hao

Abstract

Recently, there has been increasing attention towards reckoning the region of attraction (ROA) for networks. However, applying existing theory to networks with fractional-order and delays presents significant challenges. This article addresses the estimation of ROA for fractional-order complex networks with time-varying delay. Initially, two generalized fractional-order Halanay inequalities are formulated. Subsequently, leveraging the first Halanay inequality, a method for ROA estimation is developed, which is unaffected by both delay and fractional-order. However, this method tends to be conservative. To mitigate this conservatism, a delay-dependent and order-dependent ROA estimation technique is proposed based on our two developed Halanay inequalities. Additionally, numerical examples are presented to validate the proposed methodologies.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:234:y:2025:i:c:p:438-458
    DOI: 10.1016/j.matcom.2025.02.030
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    References listed on IDEAS

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    1. 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.
    2. Wang, Feng-Xian & Zhang, Jie & Shu, Yan-Jun & Liu, Xin-Ge, 2023. "On stability and event trigger control of fractional neural networks by fractional non-autonomous Halanay inequalities," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
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