### Abstract

Language | English |
---|---|

Pages | 1835-1842 |

Number of pages | 8 |

Journal | Automatica |

Volume | 46 |

Issue number | 11 |

DOIs | |

Publication status | Published - Nov 2010 |

### Fingerprint

### Keywords

- networks
- synchronization
- robustness
- systems design
- complex systems
- graph theory
- fault tolerant systems
- multi-agent systems

### Cite this

*Automatica*,

*46*(11), 1835-1842 . https://doi.org/10.1016/j.automatica.2010.06.046

}

*Automatica*, vol. 46, no. 11, pp. 1835-1842 . https://doi.org/10.1016/j.automatica.2010.06.046

**Design of highly synchronizable and robust networks.** / Estrada, Ernesto; Gago, Silvia; Caporossi, Gilles.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Design of highly synchronizable and robust networks

AU - Estrada, Ernesto

AU - Gago, Silvia

AU - Caporossi, Gilles

PY - 2010/11

Y1 - 2010/11

N2 - In this paper, the design of highly synchronizable, sparse and robust dynamical networks is addressed. Better synchronizability means faster synchronization of the oscillators, sparsity means a low ratio of links per nodes and robustness refers to the resilience of a network to the random failures or intentional removal of some of the nodes/links. Golden spectral dynamical networks (graphs) are those for which the spectral spread (the difference between the largest and smallest eigenvalues of the adjacency matrix) is equal to the spectral gap (the difference between the two largest eigenvalues of the adjacency matrix) multiplied by the square of the golden ratio. These networks display the property of “small-worldness”, are very homogeneous and have large isoperimetric (expansion) constant, together with a very high synchronizability and robustness to failures of individual oscillators. In particular, the regular bipartite dynamical networks, reported here by the first time, have the best possible expansion and consequently are the most robust ones against node/link failures or intentional attacks.

AB - In this paper, the design of highly synchronizable, sparse and robust dynamical networks is addressed. Better synchronizability means faster synchronization of the oscillators, sparsity means a low ratio of links per nodes and robustness refers to the resilience of a network to the random failures or intentional removal of some of the nodes/links. Golden spectral dynamical networks (graphs) are those for which the spectral spread (the difference between the largest and smallest eigenvalues of the adjacency matrix) is equal to the spectral gap (the difference between the two largest eigenvalues of the adjacency matrix) multiplied by the square of the golden ratio. These networks display the property of “small-worldness”, are very homogeneous and have large isoperimetric (expansion) constant, together with a very high synchronizability and robustness to failures of individual oscillators. In particular, the regular bipartite dynamical networks, reported here by the first time, have the best possible expansion and consequently are the most robust ones against node/link failures or intentional attacks.

KW - networks

KW - synchronization

KW - robustness

KW - systems design

KW - complex systems

KW - graph theory

KW - fault tolerant systems

KW - multi-agent systems

U2 - 10.1016/j.automatica.2010.06.046

DO - 10.1016/j.automatica.2010.06.046

M3 - Article

VL - 46

SP - 1835

EP - 1842

JO - Automatica

T2 - Automatica

JF - Automatica

SN - 0005-1098

IS - 11

ER -