title: Probabilistic convergence guarantees for type-II pulse-coupled oscillators.
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.
authors.affiliation: Center for Applied Mathematics, Cornell University, Ithaca, New York 14853, USA.
authors.forename: Joel
authors.initials: J
authors.lastname: Nishimura
authors.forename: Eric J
authors.initials: EJ
authors.lastname: Friedman
mesh_terms: D000465:Algorithms; D000818:Animals; D001703:Biophysics / Q000379:methods*; D003198:Computer Simulation; D015233:Models, Statistical; D008962:Models, Theoretical; D009415:Nerve Net; D009474:Neurons / Q000473:pathology; D009991:Oscillometry / Q000379:methods*; D011336:Probability