Synchronization in the Kuramoto model in presence of stochastic resetting

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.

arXiv commentInvited contribution to journal "Chaos" Special Issue "Dynamics of Oscillator Populations" edited by Arkady Pikovsky and Michael Rosenblum

References in corpus (47)

• The Kuramoto model in complex networks
• Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
• Diffusion with Stochastic Resetting
• Long Time Evolution of Phase Oscillator Systems
• First Passage Under Restart
• First order transition for the optimal search time of Lévy flights with resetting
• Exact Results for the Kuramoto Model with a Bimodal Frequency Distribution
• Optimal stochastic restart renders fluctuations in first passage times universal
• Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review
• Diffusion in a potential landscape with stochastic resetting
• Stochastic resetting in backtrack recovery by RNA polymerases
• Diffusion with stochastic resetting at power-law times
• Random walks with preferential relocations to places visited in the past and their application to biology
• Fluctuating interfaces subject to stochastic resetting
• Kuramoto model of synchronization: Equilibrium and nonequilibrium aspects
• Optimal diffusive search: nonequilibrium resetting versus equilibrium dynamics
• Stochastic thermodynamics of resetting
• Stochastic Search with Poisson and Deterministic Resetting
• Restart could optimize the probability of success in a Bernoulli trial
• First passage of a particle in a potential under stochastic resetting: a vanishing transition of optimal resetting rate
• Quantum dynamics with stochastic reset
• Statistical mechanics of the coagulation-diffusion process with a stochastic reset
• Diffusion with resetting in a logarithmic potential
• Localization transition induced by learning in random searches
• Symmetric Exclusion Process under Stochastic Resetting
• Ising model with stochastic resetting
• Active Brownian Motion in two-dimensions under Stochastic Resetting
• Sisyphus random walk
• Properties of additive functionals of Brownian motion with resetting
• Spectral content of fractional Brownian motion with stochastic reset
• Diffusion with Resetting Inside a Circle
• Resetting of fluctuating interfaces at power-law times
• Comparison of two models of tethered motion
• Diffusion with Local Resetting and Exclusion
• Controlling particle currents with evaporation and resetting from an interval
• Mitigating long transient time in deterministic systems by resetting
• Generalized splay states in phase oscillator networks
• Kuramoto model for populations of quadratic integrate-and-fire neurons with chemical and electrical coupling
• Hierarchy of exact low-dimensional reductions for populations of coupled oscillators
• Low-dimensional dynamics of phase oscillators driven by Cauchy noise
• Universal scaling and phase transitions of coupled phase oscillator populations
• A large deviation perspective on ratio observables in reset processes: robustness of rate functions
• The Kuramoto model in presence of additional interactions that break rotational symmetry
• Bifurcations in the time-delayed Kuramoto model of coupled oscillators: Exact results
• Phase diagram of noisy systems of coupled oscillators with a bimodal frequency distribution
• The Sakaguchi-Kuramoto model in presence of asymmetric interactions that break phase-shift symmetry
• The Winfree model with non-infinitesimal phase-response curve: Ott-Antonsen theory

Cited by in corpus (5)

• Exact finite-dimensional description for networks of globally coupled spiking neurons
• Condensation transition in large deviations of self-similar Gaussian processes with stochastic resetting
• Dynamics of closed quantum systems under stochastic resetting
• Biased random walk on random networks in presence of stochastic resetting: Exact results
• Influence of cumulative damage on synchronization of Kuramoto oscillators on networks