Probabilistic convergence guarantees for type-II pulse-coupled oscillators

Joel Nishimura, Eric J. Friedman

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


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
Issue number2
StatePublished - Aug 17 2012
Externally publishedYes

ASJC Scopus subject areas

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


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