Synchronization in random weighted directed networks

Maurizio Porfiri; Daniel J. Stilwell; Erik M. Bollt

doi:10.1109/TCSI.2008.925357

Synchronization in random weighted directed networks

Maurizio Porfiri, Daniel J. Stilwell, Erik M. Bollt

Mechanical and Aerospace Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

We assess synchronization of oscillators that are coupled via a time-varying stochastic network, modeled as a weighted directed random graph that switches at a given rate between a set of possible graphs. The existence of any graph edge is probabilistic and independent from the existence of any other edge. We further allow each edge to be weighted differently. Even if the network is always instantaneously not connected, we show that sufficient information is propagated through the network to allow almost sure local synchronization as long as the expected value of the network is connected, and that the switching rate is sufficiently fast.

Original language	English (US)
Pages (from-to)	3170-3177
Number of pages	8
Journal	IEEE Transactions on Circuits and Systems I: Regular Papers
Volume	55
Issue number	10
DOIs	https://doi.org/10.1109/TCSI.2008.925357
State	Published - 2008

Keywords

Ad hoc networking
Directed graphs
Fast switching
Random graphs
Synchronization
Weighted graphs

ASJC Scopus subject areas

Hardware and Architecture
Electrical and Electronic Engineering

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10.1109/TCSI.2008.925357

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title = "Synchronization in random weighted directed networks",

abstract = "We assess synchronization of oscillators that are coupled via a time-varying stochastic network, modeled as a weighted directed random graph that switches at a given rate between a set of possible graphs. The existence of any graph edge is probabilistic and independent from the existence of any other edge. We further allow each edge to be weighted differently. Even if the network is always instantaneously not connected, we show that sufficient information is propagated through the network to allow almost sure local synchronization as long as the expected value of the network is connected, and that the switching rate is sufficiently fast.",

keywords = "Ad hoc networking, Directed graphs, Fast switching, Random graphs, Synchronization, Weighted graphs",

author = "Maurizio Porfiri and Stilwell, {Daniel J.} and Bollt, {Erik M.}",

note = "Funding Information: Manuscript received May 17, 2006; revised July 2, 2007. First published April 18, 2008; current version published November 21, 2008. This work was supported in part by the National Science Foundation under Grant IIS-0238092 and by the Office of Naval Research under Grant N000140310444, Grant N000140510780, and Grant N000140510516. The work of E. M. Bollt was supported by the National Science Foundation, Applied Mathematics Division, under Grant DMS-0404778. This paper was recommended by Associate Editor R. Rovatti.",

year = "2008",

doi = "10.1109/TCSI.2008.925357",

language = "English (US)",

volume = "55",

pages = "3170--3177",

journal = "IEEE Transactions on Circuits and Systems I: Regular Papers",

issn = "1057-7122",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

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T1 - Synchronization in random weighted directed networks

AU - Porfiri, Maurizio

AU - Stilwell, Daniel J.

AU - Bollt, Erik M.

N1 - Funding Information: Manuscript received May 17, 2006; revised July 2, 2007. First published April 18, 2008; current version published November 21, 2008. This work was supported in part by the National Science Foundation under Grant IIS-0238092 and by the Office of Naval Research under Grant N000140310444, Grant N000140510780, and Grant N000140510516. The work of E. M. Bollt was supported by the National Science Foundation, Applied Mathematics Division, under Grant DMS-0404778. This paper was recommended by Associate Editor R. Rovatti.

PY - 2008

Y1 - 2008

N2 - We assess synchronization of oscillators that are coupled via a time-varying stochastic network, modeled as a weighted directed random graph that switches at a given rate between a set of possible graphs. The existence of any graph edge is probabilistic and independent from the existence of any other edge. We further allow each edge to be weighted differently. Even if the network is always instantaneously not connected, we show that sufficient information is propagated through the network to allow almost sure local synchronization as long as the expected value of the network is connected, and that the switching rate is sufficiently fast.

AB - We assess synchronization of oscillators that are coupled via a time-varying stochastic network, modeled as a weighted directed random graph that switches at a given rate between a set of possible graphs. The existence of any graph edge is probabilistic and independent from the existence of any other edge. We further allow each edge to be weighted differently. Even if the network is always instantaneously not connected, we show that sufficient information is propagated through the network to allow almost sure local synchronization as long as the expected value of the network is connected, and that the switching rate is sufficiently fast.

KW - Ad hoc networking

KW - Directed graphs

KW - Fast switching

KW - Random graphs

KW - Synchronization

KW - Weighted graphs

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DO - 10.1109/TCSI.2008.925357

M3 - Article

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JO - IEEE Transactions on Circuits and Systems I: Regular Papers

JF - IEEE Transactions on Circuits and Systems I: Regular Papers

IS - 10

ER -

Synchronization in random weighted directed networks

Abstract

Keywords

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