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 language||English (US)|
|Journal||Physical Review E - Statistical, Nonlinear, and Soft Matter Physics|
|State||Published - Aug 17 2012|
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics