Kick synchronization versus diffusive synchronization

TL;DR

This paper compares two primary models of oscillator synchronization, highlighting their differences and similarities, especially in weak coupling scenarios, to deepen understanding of synchronization mechanisms.

Contribution

It provides an introductory analysis contrasting diffusive and kick synchronization models, emphasizing their fundamental differences and analogies in weak coupling regimes.

Findings

Diffusive and kick models use different contraction measures.

Weak coupling reveals important analogies between models.

Fundamental differences influence synchronization analysis.

Abstract

The paper provides an introductory discussion about two fundamental models of oscillator synchronization: the (continuous-time) diffusive model, that dominates the mathematical literature on synchronization, and the (hybrid) kick model, that accounts for most popular examples of synchronization, but for which only few theoretical results exist. The paper stresses fundamental differences between the two models, such as the different contraction measures underlying the analysis, as well as important analogies that can be drawn in the limit of weak coupling.