Analytical approach to subsystem resetting in generalized Kuramoto models

TL;DR

This paper develops a theoretical framework for analyzing subsystem resetting in Kuramoto models, revealing how partial resets influence synchronization and phase transitions in nonequilibrium oscillator systems.

Contribution

It introduces a continued-fraction approach to derive self-consistent equations for stationary states under subsystem resetting, extending analysis to noisy and noiseless dynamics with arbitrary interactions.

Findings

Subsystem resetting can shift or suppress synchronization transitions.

Resetting can induce re-entrant behavior and phase boundary restructuring.

Framework recovers known results and extends to general settings.

Abstract

Stochastic resetting has emerged as a powerful mechanism for driving systems into nonequilibrium stationary states with tunable properties. While most existing studies focus on global resetting, where all degrees of freedom are simultaneously reset, recent work has shown that resetting only a subset of degrees of freedom (subsystem resetting) can qualitatively alter collective behavior in interacting many-body systems. In this work, we develop a general theoretical framework for analysing subsystem resetting in Kuramoto-type coupled-oscillator systems. Building on a continued-fraction approach, we derive self-consistent equations for the stationary-state order parameter of the non-reset subsystem, applicable to both noisy and noiseless dynamics and to models with arbitrary interaction harmonics. Using this framework, we systematically investigate how the stationary state and phase transitions depend on the resetting rate, the size of the reset subsystem, and the reset configuration. We show that subsystem resetting can shift or even suppress synchronization transitions, and can give rise to nontrivial features such as re-entrant behavior and restructuring of phase boundaries. In specific cases, including the noiseless Kuramoto model with a Lorentzian frequency distribution, our results recover known analytical predictions and extend them to more general settings. These results establish subsystem resetting as a versatile control protocol for engineering collective dynamics in nonequilibrium interacting systems.