Synchronization Phenomenon in Three-Time-Scale Systems

TL;DR

This paper develops a mathematical framework to analyze synchronization in three-time-scale coupled oscillator networks, providing conditions for stable synchronization considering heterogeneity and coupling strength.

Contribution

It introduces a novel analytical approach for synchronization in multi-time-scale systems with canard dynamics, addressing heterogeneity and stability criteria.

Findings

Derived a sufficient condition for synchronization error to decrease below a threshold

Established the impact of coupling strength and heterogeneity on synchronization stability

Supported results with rigorous mathematical analysis

Abstract

This paper investigates synchronization phenomena in networks of coupled oscillators governed by three-time-scale dynamical systems exhibiting canard dynamics. A mathematical framework has been developed to analyze the synchronization of fast variables across heterogeneous systems, deriving a sufficient condition for the synchronization error to fall below a specified threshold within the minimum linger time. This condition accounts for coupling strength, heterogeneity, and time-scale separation, ensuring stable oscillatory behavior in the network. The result, supported by rigorous mathematical analysis, advances the understanding of synchronization in complex multi-time-scale systems.