Probabilistic Convergence Guarantees for Type II Pulse Coupled Oscillators

Autor:	Nishimura, Joel, Friedman, Eric J.
Rok vydání:	2012
Předmět:	Mathematics - Dynamical Systems Nonlinear Sciences - Adaptation and Self-Organizing Systems
Zdroj:	Phys. Rev. E 86, 025201(R) (2012)
Druh dokumentu:	Working Paper
DOI:	10.1103/PhysRevE.86.025201
Popis:	We show that a large class of pulse coupled oscillators converge with high probability from random initial conditions on a large class of graphs with time delays. Our analysis combines previous local convergence results, probabilistic network analysis, and a new classification scheme for Type II phase response curves to produce rigorous lower bounds for convergence probabilities based on network density. These bounds are then used to develop a simple, fast and rigorous computational analytic technique. These results suggest new methods for the analysis of pulse coupled oscillators, and provide new insights into the operation of biological Type II phase response curves and also the design of decentralized and minimal clock synchronization schemes in sensor nets. Comment: 5 pages, 3 figures, for submission to PRL
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1204.3209 Zobrazit plný text záznamu View this record from Arxiv