Probabilistic convergence guarantees for type-II pulse-coupled oscillators

Joel Nishimura, Eric J. Friedman

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Article number025201
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume86
Issue number2
DOIs
StatePublished - Aug 17 2012
Externally publishedYes

Fingerprint

phase response
Coupled Oscillators
oscillators
Clock Synchronization
network analysis
Curve
Probabilistic Analysis
Local Convergence
Network Analysis
curves
pulses
Convergence Results
clocks
Decentralized
Time Delay
synchronism
Initial conditions
time lag
Excitation
Lower bound

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

Cite this

Probabilistic convergence guarantees for type-II pulse-coupled oscillators. / Nishimura, Joel; Friedman, Eric J.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 86, No. 2, 025201, 17.08.2012.

Research output: Contribution to journalArticle

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