Synchronization in the Kuramoto model in presence of stochastic resetting

TL;DR

This paper investigates how stochastic resetting affects the Kuramoto model, revealing that resetting can induce synchronization even in regimes where the original model does not support it, using analytical and numerical methods.

Contribution

It demonstrates that stochastic resetting can fundamentally alter the phase diagram of the Kuramoto model, enabling synchronization through a simple resetting protocol.

Findings

Resetting can induce synchronization in non-synchronized regimes.

The phase diagram is significantly modified by resetting protocols.

Exact analysis using Ott-Antonsen ansatz supports the results.

Abstract

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 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.