### Abstract

Original language | English |
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Pages (from-to) | 1395-1416 |

Number of pages | 22 |

Journal | SIAM Journal on Control and Optimization |

Volume | 51 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2013 |

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### Cite this

*SIAM Journal on Control and Optimization*,

*51*(2), 1395-1416. https://doi.org/10.1137/100781699

**Synchronization via pinning control on general complex networks.** / Yu, Wenwu; Chen, Guanrong; Lu, Jinhu; Kurths, Juergen.

Research output: Contribution to journal › Article

*SIAM Journal on Control and Optimization*, vol. 51, no. 2, pp. 1395-1416. https://doi.org/10.1137/100781699

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TY - JOUR

T1 - Synchronization via pinning control on general complex networks

AU - Yu, Wenwu

AU - Chen, Guanrong

AU - Lu, Jinhu

AU - Kurths, Juergen

PY - 2013

Y1 - 2013

N2 - This paper studies synchronization via pinning control on general complex dynamical networks, such as strongly connected networks, networks with a directed spanning tree, weakly connected networks, and directed forests. A criterion for ensuring network synchronization on strongly connected networks is given. It is found that the vertices with very small in-degrees should be pinned first. In addition, it is shown that the original condition with controllers can be reformulated such that it does not depend on the form of the chosen controllers, which implies that the vertices with very large out-degrees may be pinned. Then, a criterion for achieving synchronization on networks with a directed spanning tree, which can be composed of many strongly connected components, is derived. It is found that the strongly connected components with very few connections from other components should be controlled and the components with many connections from other components can achieve synchronization even without controls. Moreover, a simple but effective pinning algorithm for reaching synchronization on a general complex dynamical network is proposed. Finally, some simulation examples are given to verify the proposed pinning scheme.

AB - This paper studies synchronization via pinning control on general complex dynamical networks, such as strongly connected networks, networks with a directed spanning tree, weakly connected networks, and directed forests. A criterion for ensuring network synchronization on strongly connected networks is given. It is found that the vertices with very small in-degrees should be pinned first. In addition, it is shown that the original condition with controllers can be reformulated such that it does not depend on the form of the chosen controllers, which implies that the vertices with very large out-degrees may be pinned. Then, a criterion for achieving synchronization on networks with a directed spanning tree, which can be composed of many strongly connected components, is derived. It is found that the strongly connected components with very few connections from other components should be controlled and the components with many connections from other components can achieve synchronization even without controls. Moreover, a simple but effective pinning algorithm for reaching synchronization on a general complex dynamical network is proposed. Finally, some simulation examples are given to verify the proposed pinning scheme.

U2 - 10.1137/100781699

DO - 10.1137/100781699

M3 - Article

VL - 51

SP - 1395

EP - 1416

JO - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

SN - 0363-0129

IS - 2

ER -