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Contraction theory based cluster synchronization in switched networks via pinning impulsive control with time-varying delays

Author

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  • Chauhan, Yashasvi
  • Sharma, B.B.

Abstract

This paper studies cluster synchronization in switched complex networks using a pinning impulsive control strategy. By utilizing the squared differential length within the contraction theory framework, the proposed method ensures exponential convergence, offering an efficient tool for stability and synchronization analysis in complex networks. Unlike traditional methods that require impulsive control to coincide with switching events, the proposed approach introduces mode-dependent impulsive effects while allowing impulsive actions to occur independently of switching, providing greater flexibility in control design. The concept of a mode-dependent average impulsive interval (MDAII) is employed, which assigns distinct impulsive intervals to each mode, thereby enhancing both control flexibility and efficiency. By considering system and coupling delays and combining the MDAII with a mode-dependent average dwell time (MDADT) strategy, we derive Lyapunov functionals to establish synchronization criteria. These criteria depend on impulsive control gains, delay parameters, and mode transitions. The effectiveness of the framework is demonstrated through numerical examples, including artificial neural networks, Hindmarsh-Rose neuronal oscillators, and Kuromoto oscillator network highlighting its practical applicability.

Suggested Citation

  • Chauhan, Yashasvi & Sharma, B.B., 2026. "Contraction theory based cluster synchronization in switched networks via pinning impulsive control with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 513(C).
    • Handle: RePEc:eee:apmaco:v:513:y:2026:i:c:s0096300325005132
    DOI: 10.1016/j.amc.2025.129788
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    References listed on IDEAS

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    1. Fan, Hongguang & Shi, Kaibo & Zhao, Yi, 2022. "Pinning impulsive cluster synchronization of uncertain complex dynamical networks with multiple time-varying delays and impulsive effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 587(C).
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    8. Guo, Junfeng & Wang, Fei & Xue, Qianwen & Wang, Mengqing, 2023. "Cluster synchronization control for coupled genetic oscillator networks under denial-of-service attacks: Pinning partial impulsive strategy," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
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