Publication Details
Title: Probabilistic Convergence Guarantees for Type-II Pulse-Coupled Oscillators
Author: J. Nishimura and E. Friedman
Group: Algorithms
Date: August 2012
PDF: [Not available online]
Overview:
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.
Bibliographic Information:
Physical Review E, Vol. 86, Issue 2
Bibliographic Reference:
J. Nishimura and E. Friedman. Probabilistic Convergence Guarantees for Type-II Pulse-Coupled Oscillators. Physical Review E, Vol. 86, Issue 2, August 2012
Author: J. Nishimura and E. Friedman
Group: Algorithms
Date: August 2012
PDF: [Not available online]
Overview:
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.
Bibliographic Information:
Physical Review E, Vol. 86, Issue 2
Bibliographic Reference:
J. Nishimura and E. Friedman. Probabilistic Convergence Guarantees for Type-II Pulse-Coupled Oscillators. Physical Review E, Vol. 86, Issue 2, August 2012