### 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 synchronization as long as the expected value of the network is connected, and that the switching rate is sufficiently fast.

Original language | English (US) |
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Title of host publication | Proceedings of the 2007 American Control Conference, ACC |

Pages | 2387-2392 |

Number of pages | 6 |

DOIs | |

State | Published - 2007 |

Event | 2007 American Control Conference, ACC - New York, NY, United States Duration: Jul 9 2007 → Jul 13 2007 |

### Other

Other | 2007 American Control Conference, ACC |
---|---|

Country | United States |

City | New York, NY |

Period | 7/9/07 → 7/13/07 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Control and Systems Engineering

### Cite this

*Proceedings of the 2007 American Control Conference, ACC*(pp. 2387-2392). [4282570] https://doi.org/10.1109/ACC.2007.4282570

**Stochastic synchronization over weighted directed networks.** / Porfiri, Maurizio; Stilwell, Daniel J.; Bollt, Erik M.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 2007 American Control Conference, ACC.*, 4282570, pp. 2387-2392, 2007 American Control Conference, ACC, New York, NY, United States, 7/9/07. https://doi.org/10.1109/ACC.2007.4282570

}

TY - GEN

T1 - Stochastic synchronization over weighted directed networks

AU - Porfiri, Maurizio

AU - Stilwell, Daniel J.

AU - Bollt, Erik M.

PY - 2007

Y1 - 2007

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 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 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

UR - http://www.scopus.com/inward/record.url?scp=46449120055&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=46449120055&partnerID=8YFLogxK

U2 - 10.1109/ACC.2007.4282570

DO - 10.1109/ACC.2007.4282570

M3 - Conference contribution

AN - SCOPUS:46449120055

SN - 1424409888

SN - 9781424409884

SP - 2387

EP - 2392

BT - Proceedings of the 2007 American Control Conference, ACC

ER -