TY - JOUR
T1 - Probabilistic convergence guarantees for type-II pulse-coupled oscillators
AU - Nishimura, Joel
AU - Friedman, Eric J.
N1 - Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.
PY - 2012/8/17
Y1 - 2012/8/17
N2 - 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 classification scheme for type-II phase response curves to produce rigorous lower bounds for convergence probabilities based on network density. These results suggest methods for the analysis of pulse-coupled oscillators, and provide insights into the balance of excitation and inhibition in the operation of biological type-II phase response curves and also the design of decentralized and minimal clock synchronization schemes in sensor nets.
AB - 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 classification scheme for type-II phase response curves to produce rigorous lower bounds for convergence probabilities based on network density. These results suggest methods for the analysis of pulse-coupled oscillators, and provide insights into the balance of excitation and inhibition in the operation of biological type-II phase response curves and also the design of decentralized and minimal clock synchronization schemes in sensor nets.
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U2 - 10.1103/PhysRevE.86.025201
DO - 10.1103/PhysRevE.86.025201
M3 - Article
AN - SCOPUS:84865315243
VL - 86
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
SN - 1539-3755
IS - 2
M1 - 025201
ER -