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Kuramoto Model with Delay: The Role of the Frequency Distribution

Author

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  • Vladimir V. Klinshov

    (A. V. Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences, 46 Ul’yanov Street, 603950 Nizhny Novgorod, Russia
    Faculty of Radiophysics of Nizhny Novgorod, Lobachevsky State University, 23 Prospekt Gagarina, 603022 Nizhny Novgorod, Russia
    Leonhard Euler International Mathematical Institute, Saint Petersburg University, 7-9 Universitetskaya Embankment, 199034 St. Petersburg, Russia
    National Research University Higher School of Economics, 25/12 Bol’shaya Pecherskaya Street, 603155 Nizhny Novgorod, Russia)

  • Alexander A. Zlobin

    (A. V. Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences, 46 Ul’yanov Street, 603950 Nizhny Novgorod, Russia
    Faculty of Radiophysics of Nizhny Novgorod, Lobachevsky State University, 23 Prospekt Gagarina, 603022 Nizhny Novgorod, Russia
    Leonhard Euler International Mathematical Institute, Saint Petersburg University, 7-9 Universitetskaya Embankment, 199034 St. Petersburg, Russia)

Abstract

The Kuramoto model is a classical model used for the describing of synchronization in populations of oscillatory units. In the present paper we study the Kuramoto model with delay with a focus on the distribution of the oscillators’ frequencies. We consider a series of rational distributions which allow us to reduce the population dynamics to a set of several delay differential equations. We use the bifurcation analysis of these equations to study the transition from the asynchronous to synchronous state. We demonstrate that the form of the frequency distribution may play a substantial role in synchronization. In particular, for Lorentzian distribution the delay prevents synchronization, while for other distributions the delay can facilitate synchronization.

Suggested Citation

  • Vladimir V. Klinshov & Alexander A. Zlobin, 2023. "Kuramoto Model with Delay: The Role of the Frequency Distribution," Mathematics, MDPI, vol. 11(10), pages 1-11, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2325-:d:1148469
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    References listed on IDEAS

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    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.
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