Phase-shift inversion in oscillator systems with periodically switching couplings

TL;DR

This paper explores how the synchronization transition in oscillator systems with periodically changing couplings can be detected through phase-shift inversion, revealing critical dynamics and diverging relaxation times near the transition.

Contribution

It demonstrates that phase-shift inversion in oscillator systems with switching interactions signals the synchronization phase transition, linking temporal response to topological dynamics.

Findings

Phase-shift inversion occurs near the critical point.

The order parameter can be larger at minimum interaction density.

Diverging relaxation time causes the phase-shift inversion.

Abstract

A system's response to external periodic changes can provide crucial information about its dynamical properties. We investigate the synchronization transition, an archetypical example of a dynamic phase transition, in the framework of such a temporal response. The Kuramoto model under periodically switching interactions has the same type of phase transition as the original mean-field model. Furthermore, we see that the signature of the synchronization transition appears in the relative delay of the order parameter with respect to the phase of oscillating interactions as well. Specifically, the phase shift becomes significantly larger as the system gets closer to the phase transition so that the order parameter at the minimum interaction density can even be larger than that at the maximum interaction density, counterintuitively. We argue that this phase-shift inversion is caused by the diverging relaxation time, in a similar way to the resonance near the critical point in the kinetic Ising model. Our result, based on exhaustive simulations on globally coupled systems as well as scale-free networks, shows that an oscillator system's phase transition can be manifested in the temporal response to the topological dynamics of the underlying connection structure.