Paper Info
Title
Global Analysis of a Continuum Model for Monotone Pulse-Coupled Oscillators.
Abstract
We consider a continuum of phase oscillators on the circle interacting through an impulsive instantaneous coupling. In contrast with previous studies on related pulse-coupled models, the stability results obtained in the continuum limit are global. For the nonlinear transport equation governing the evolution of the oscillators, we propose (under technical assumptions) a global Lyapunov function which is induced by a total variation distance between quantile densities. The monotone time evolution of the Lyapunov function completely characterizes the dichotomic behavior of the oscillators: either the oscillators converge in finite time to a synchronous state or they asymptotically converge to an asynchronous state uniformly spread on the circle. The results of the present paper apply to popular phase oscillators models (e.g., the well-known leaky integrate-and-fire model) and show a strong parallel between the analysis of finite and infinite populations. In addition, they provide a novel approach for the (global) analysis of pulse-coupled oscillators.
Year
DOI
Venue
2013
10.1109/TAC.2012.2229811
Automatic Control, IEEE Transactions
Keywords
Field
DocType
Oscillators,Couplings,Sociology,Statistics,Mathematical model,Equations,Lyapunov methods
Total variation,Lyapunov function,Convection–diffusion equation,Mathematical optimization,Nonlinear system,Control theory,Mathematical analysis,Continuum mechanics,Time evolution,Partial differential equation,Mathematics,Monotone polygon
Journal
Volume
Issue
ISSN
58
5
0018-9286
Citations 
PageRank 
References 
5
0.42
5
Authors
2
Name
Order
Citations
PageRank
Alexandre Mauroy1598.21
Rodolphe Sepulchre21478140.85