Normal hyperbolicity for non-autonomous oscillators and oscillator 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.