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 new classification scheme for Type II phase response curves to produce rigorous lower bounds for convergence probabilities based on network density. These bounds are then used to develop a simple, fast and rigorous computational analytic technique. These results suggest new methods for the analysis of pulse coupled oscillators, and provide new insights into the operation of biological Type II phase response curves and also the design of decentralized and minimal clock synchronization schemes in sensor nets.

5 pages, 3 figures, for submission to PRL

References in corpus (3)

• The type II phase resetting curve is optimal for stochastic synchrony
• The simplest problem in the collective dynamics of neural networks: Is synchrony stable?
• Robust convergence in pulse coupled oscillators with delays

Cited by in corpus (7)

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• Frequency adjustment and synchrony in networks of delayed pulse coupled oscillators
• Percolation critical exponents in cluster kinetics of pulse-coupled oscillators
• Scalable Resetting Algorithms for Synchronization of Pulse-Coupled Oscillators over Rooted Directed Graphs
• An Attack-Resilient Pulse-Based Synchronization Strategy for General Connected Topologies