Synchronization induced by stochastic subsystem resetting in complex networks

Abstract

We study synchronization in network-coupled oscillators subject to stochastic resetting of a subset of nodes. We show that resetting can induce collective coherence in oscillators that are never directly reset, through the interplay of network structure, frequency heterogeneity, and the organization of the reset subsystem. In the infinite-resetting-rate limit, the reset nodes become effectively pinned to a reference phase, and linearization near synchronization maps the dynamics of the remaining subsystem onto a grounded-Laplacian problem. This formulation yields an analytical relation between the synchronization level and the reset parameters, providing an estimate of the coupling strength required to achieve a prescribed degree of coherence. Beyond the linear regime, we develop a mean-field description in which the reset subsystem acts as an effective ordering field for the remaining oscillators. Numerical simulations across different network topologies confirm these predictions and show that synchronization is enhanced by increasing both the reset fraction and network connectivity. In heterogeneous networks, the placement of reset nodes can strongly influence the synchronization response. For frequency distributions with nonzero mean, resetting competes with the intrinsic collective rotation and can drive the system from a rotating synchronized state to a phase-locked state. These results establish subsystem resetting as a mechanism for inducing and controlling collective synchronization in complex networks.