### Abstract

There has been mounting evidence that many types of biological or technological networks possess a clustered structure. As many system functions depend on synchronization, it is important to investigate the synchronizability of complex clustered networks. Here we focus on one fundamental question: Under what condition can the network synchronizability be optimized? In particular, since the two basic parameters characterizing a complex clustered network are the probabilities of intercluster and intracluster connections, we investigate, in the corresponding two-dimensional parameter plane, regions where the network can be best synchronized. Our study yields a quite surprising finding: a complex clustered network is most synchronizable when the two probabilities match each other approximately. Mismatch, for instance caused by an overwhelming increase in the number of intracluster links, can counterintuitively suppress or even destroy synchronization, even though such an increase tends to reduce the average network distance. This phenomenon provides possible principles for optimal synchronization on complex clustered networks. We provide extensive numerical evidence and an analytic theory to establish the generality of this phenomenon. (C) 2008 American Institute of Physics.

Original language | English |
---|---|

Article number | 013101 |

Number of pages | 10 |

Journal | Chaos |

Volume | 18 |

Issue number | 1 |

DOIs | |

Publication status | Published - Mar 2008 |

### Keywords

- small-world networks
- characteristic vectors
- infinite dimensions
- molecular networks
- dynamical networks
- bordered matrices
- protein complexes
- organization
- oscillator
- pathways

### Cite this

*Chaos*,

*18*(1), [013101]. https://doi.org/10.1063/1.2826289

**Optimization of synchronization in complex clustered networks.** / Huang, Liang; Lai, Ying-Cheng; Gatenby, Robert A.

Research output: Contribution to journal › Article

*Chaos*, vol. 18, no. 1, 013101. https://doi.org/10.1063/1.2826289

}

TY - JOUR

T1 - Optimization of synchronization in complex clustered networks

AU - Huang, Liang

AU - Lai, Ying-Cheng

AU - Gatenby, Robert A.

PY - 2008/3

Y1 - 2008/3

N2 - There has been mounting evidence that many types of biological or technological networks possess a clustered structure. As many system functions depend on synchronization, it is important to investigate the synchronizability of complex clustered networks. Here we focus on one fundamental question: Under what condition can the network synchronizability be optimized? In particular, since the two basic parameters characterizing a complex clustered network are the probabilities of intercluster and intracluster connections, we investigate, in the corresponding two-dimensional parameter plane, regions where the network can be best synchronized. Our study yields a quite surprising finding: a complex clustered network is most synchronizable when the two probabilities match each other approximately. Mismatch, for instance caused by an overwhelming increase in the number of intracluster links, can counterintuitively suppress or even destroy synchronization, even though such an increase tends to reduce the average network distance. This phenomenon provides possible principles for optimal synchronization on complex clustered networks. We provide extensive numerical evidence and an analytic theory to establish the generality of this phenomenon. (C) 2008 American Institute of Physics.

AB - There has been mounting evidence that many types of biological or technological networks possess a clustered structure. As many system functions depend on synchronization, it is important to investigate the synchronizability of complex clustered networks. Here we focus on one fundamental question: Under what condition can the network synchronizability be optimized? In particular, since the two basic parameters characterizing a complex clustered network are the probabilities of intercluster and intracluster connections, we investigate, in the corresponding two-dimensional parameter plane, regions where the network can be best synchronized. Our study yields a quite surprising finding: a complex clustered network is most synchronizable when the two probabilities match each other approximately. Mismatch, for instance caused by an overwhelming increase in the number of intracluster links, can counterintuitively suppress or even destroy synchronization, even though such an increase tends to reduce the average network distance. This phenomenon provides possible principles for optimal synchronization on complex clustered networks. We provide extensive numerical evidence and an analytic theory to establish the generality of this phenomenon. (C) 2008 American Institute of Physics.

KW - small-world networks

KW - characteristic vectors

KW - infinite dimensions

KW - molecular networks

KW - dynamical networks

KW - bordered matrices

KW - protein complexes

KW - organization

KW - oscillator

KW - pathways

U2 - 10.1063/1.2826289

DO - 10.1063/1.2826289

M3 - Article

VL - 18

JO - Chaos

JF - Chaos

SN - 1054-1500

IS - 1

M1 - 013101

ER -