### Abstract

Synchronization in networks with different topologies is studied. We show that for a large class of oscillators there exist two classes of networks; class-A: networks for which the condition of stable synchronous state is σγ_{2} > a, and class-B: networks for which this condition reads γN/γ_{2} < b, where a and b are constants that depend on local dynamics, synchronous state and the coupling matrix, but not on the Laplacian matrix of the graph describing the topology of the network. Here γ1 = 0 < γ_{2} < . . . < γN are the eigenvalues of the Laplacian matrix, where N is the order of the graph. Synchronization in networks whose topology is described by classical random graphs and power-law random graphs when N → ∞ is investigated in detail.

Original language | English |
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Title of host publication | ISCAS 2006 |

Subtitle of host publication | 2006 IEEE International Symposium on Circuits and Systems, Proceedings |

Pages | 2641-2644 |

Number of pages | 4 |

Publication status | Published - Dec 1 2006 |

Event | ISCAS 2006: 2006 IEEE International Symposium on Circuits and Systems - Kos, Greece Duration: May 21 2006 → May 24 2006 |

### Publication series

Name | Proceedings - IEEE International Symposium on Circuits and Systems |
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ISSN (Print) | 0271-4310 |

### Other

Other | ISCAS 2006: 2006 IEEE International Symposium on Circuits and Systems |
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Country | Greece |

City | Kos |

Period | 5/21/06 → 5/24/06 |

### Fingerprint

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

*ISCAS 2006: 2006 IEEE International Symposium on Circuits and Systems, Proceedings*(pp. 2641-2644). [1693166] (Proceedings - IEEE International Symposium on Circuits and Systems).