Exponential synchronization of the Kuramoto model with inertia and frustration under locally coupled network

TL;DR

This paper establishes conditions under which the Kuramoto model with inertia and frustration achieves exponential synchronization on symmetric networks, using energy functionals to control phase and frequency behaviors.

Contribution

It provides a new theoretical framework for exponential synchronization considering inertia and frustration effects in the Kuramoto model on symmetric networks.

Findings

Phase diameter becomes uniformly bounded after finite time.

Frequency diameter decays exponentially to zero.

Energy functionals effectively control dissipation processes.

Abstract

We study the collective synchronized behavior of the Kuramoto model with inertia and frustration effects on a connected and symmetric network. We aim to establish sufficient frameworks for achieving complete frequency synchronization, taking into account initial configuration, small inertia and frustration, and large coupling strength. More precisely, we first demonstrate that the phase diameter will be uniformly bounded by a small value after a finite time. Then we prove that the frequency diameter exhibits exponential decay to zero. Our approach relies on a careful construction of energy functionals, which effectively control the dissipation of phase and frequency diameters.