Kick synchronization versus diffusive synchronization

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.

Correction of a mistake in Definition 1

References in corpus (2)

• Stability of the splay state in pulse--coupled networks
• Contraction of monotone phase-coupled oscillators

Cited by in corpus (6)

• Mathematical frameworks for oscillatory network dynamics in neuroscience
• Sensitivity analysis of oscillator models in the space of phase-response curves: Oscillators as open systems
• Rapid and robust synchronization via weak synaptic coupling Extended arXiv version
• Singularly perturbed phase response curves
• Global Practical Node and Edge Synchronization in Kuramoto Networks: A Submodular Optimization Framework
• Uncovering Droop Control Laws Embedded Within the Nonlinear Dynamics of Van der Pol Oscillators