Synchronization of coupled limit cycles

TL;DR

This paper introduces a unified method for analyzing synchronization in coupled autonomous systems, providing a sufficient condition based on geometric properties and coupling operators, applicable across physics and biology models.

Contribution

It offers a novel, general framework for synchronization analysis using variational equations and geometric properties, extending applicability to various differential equation models.

Findings

Established a sufficient condition for synchronization

Applied the theory to neuron compartmental models

Validated results with numerical simulations

Abstract

A unified approach for analyzing synchronization in coupled systems of autonomous differential equations is presented in this work. Through a careful analysis of the variational equation of the coupled system we establish a sufficient condition for synchronization in terms of the geometric properties of the local limit cycles and the coupling operator. This result applies to a large class of differential equation models in physics and biology. The stability analysis is complemented with a discussion of numerical simulations of a compartmental model of a neuron.