What happens when the paradigmatic Kuramoto model involving interacting oscillators of distributed natural frequencies and showing spontaneous collective synchronization in the stationary state is subject to random and repeated interruptions of its dynamics with a reset to the initial condition? While resetting to a synchronized state, it may happen between two successive resets that the system desynchronizes, which depends on the duration of the random time interval between the two resets. Here, we unveil how such a protocol of stochastic resetting dramatically modifies the phase diagram of the bare model, allowing, in particular, for the emergence of a synchronized phase even in parameter regimes for which the bare model does not support such a phase. Our results are based on an exact analysis invoking the celebrated Ott–Antonsen ansatz for the case of the Lorentzian distribution of natural frequencies and numerical results for Gaussian frequency distribution. Our work provides a simple protocol to induce global synchrony in the system through stochastic resetting.
Synchronization in the Kuramoto model in presence of stochastic resetting
Note: This article is part of the Focus Issue, Dynamics of Oscillator Populations.
Mrinal Sarkar, Shamik Gupta; Synchronization in the Kuramoto model in presence of stochastic resetting. Chaos 1 July 2022; 32 (7): 073109. https://doi.org/10.1063/5.0090861
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