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Global synchronization of partially forced Kuramoto oscillators on networks

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  • Moreira, Carolina A.
  • de Aguiar, Marcus A.M.

Abstract

We study the synchronization of Kuramoto oscillators on networks where only a fraction of them is subjected to a periodic external force. When all oscillators receive the external drive the system always synchronize with the periodic force if its intensity is sufficiently large. Our goal is to understand the conditions for global synchronization as a function of the fraction of nodes being forced and how these conditions depend on network topology, strength of internal couplings and intensity of external forcing. Numerical simulations show that the force required to synchronize the network with the external drive increases as the inverse of the fraction of forced nodes. However, for a given coupling strength, synchronization does not occur below a critical fraction, no matter how large is the force. Network topology and properties of the forced nodes also affect the critical force for synchronization. We develop analytical calculations for the critical force for synchronization as a function of the fraction of forced oscillators and for the critical fraction as a function of coupling strength. We also describe the transition from synchronization with the external drive to spontaneous synchronization.

Suggested Citation

  • Moreira, Carolina A. & de Aguiar, Marcus A.M., 2019. "Global synchronization of partially forced Kuramoto oscillators on networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 487-496.
    • Handle: RePEc:eee:phsmap:v:514:y:2019:i:c:p:487-496
    DOI: 10.1016/j.physa.2018.09.096
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    References listed on IDEAS

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    1. Yang-Yu Liu & Jean-Jacques Slotine & Albert-László Barabási, 2011. "Controllability of complex networks," Nature, Nature, vol. 473(7346), pages 167-173, May.
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    Cited by:

    1. Dharma Raj Khatiwada, 2022. "Numerical Solution of Finite Kuramoto Model with Time-Dependent Coupling Strength: Addressing Synchronization Events of Nature," Mathematics, MDPI, vol. 10(19), pages 1-10, October.
    2. Liu, Xinmiao & Xia, Jianwei & Huang, Xia & Shen, Hao, 2020. "Generalized synchronization for coupled Markovian neural networks subject to randomly occurring parameter uncertainties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    3. Alexander Tselykh & Vladislav Vasilev & Larisa Tselykh & Fernando A. F. Ferreira, 2022. "Influence control method on directed weighted signed graphs with deterministic causality," Annals of Operations Research, Springer, vol. 311(2), pages 1281-1305, April.
    4. Barioni, Ana Elisa D. & de Aguiar, Marcus A.M., 2021. "Complexity reduction in the 3D Kuramoto model," Chaos, Solitons & Fractals, Elsevier, vol. 149(C).
    5. Cui, Qian & Li, Lulu & Cao, Jinde & Alsaadi, Fawaz E., 2022. "Synchronization of Kuramoto-oscillator networks under event-triggered delayed impulsive control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P1).

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