Contraction of monotone phase-coupled oscillators

TL;DR

This paper proves a global contraction property for networks of monotone phase-coupled oscillators using total variation distance, which predicts whether the network synchronizes or converges to a splay state.

Contribution

It introduces a contraction analysis for monotone phase-coupled oscillators, linking the contraction property to the network's long-term behavior.

Findings

Networks either synchronize in finite time or converge to a splay state.

Contraction measure is based on total variation distance.

Provides a unified framework for analyzing oscillator network dynamics.

Abstract

This paper establishes a global contraction property for networks of phase-coupled oscillators characterized by a monotone coupling function. The contraction measure is a total variation distance. The contraction property determines the asymptotic behavior of the network, which is either finite-time synchronization or asymptotic convergence to a splay state.