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.
| Original language | English (US) |
|---|---|
| Article number | 025201 |
| Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |
| Volume | 86 |
| Issue number | 2 |
| DOIs | |
| State | Published - Aug 17 2012 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Condensed Matter Physics
- Statistical and Nonlinear Physics
- Statistics and Probability
Cite this
Probabilistic convergence guarantees for type-II pulse-coupled oscillators. / Nishimura, Joel; Friedman, Eric J.
In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 86, No. 2, 025201, 17.08.2012.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Probabilistic convergence guarantees for type-II pulse-coupled oscillators
AU - Nishimura, Joel
AU - Friedman, Eric J.
PY - 2012/8/17
Y1 - 2012/8/17
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84865315243&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84865315243&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.86.025201
DO - 10.1103/PhysRevE.86.025201
M3 - Article
VL - 86
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
SN - 1539-3755
IS - 2
M1 - 025201
ER -