Normal hyperbolicity for non-autonomous oscillators and oscillator networks

TL;DR

This paper explores the concept of normal hyperbolicity in non-autonomous oscillators and networks, providing a framework to understand synchronization and chronotaxic systems through a mapping approach and hierarchical aggregation.

Contribution

It introduces a novel perspective on non-autonomous oscillators using normal hyperbolicity, encompassing chronotaxic systems and hierarchical network analysis.

Findings

Framework for understanding oscillator synchronization

Inclusion of chronotaxic systems in the model

Hierarchical aggregation scheme for networks

Abstract

This chapter presents a view of a non-autonomous oscillator as a mapping from input functions of time to a circle of possible solutions (state functions of time). It indicates how this view encompasses chronotaxic systems and enables one, at least conceptually, to understand the extent of synchronisation in networks of oscillators, whether autonomous or not. For the latter a hierarchical aggregation scheme is introduced. The approach is based on the theory of normal hyperbolicity.