Cluster synchronization in fractional-order complex dynamical networks

CHEN Liping; CHAI Yi; WU Ranchao; SUN Jian

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Cluster synchronization in fractional-order complex dynamical networks

CHEN Liping 1,CHAI Yi 1 *,WU Ranchao 2,SUN Jian 1

1.School of Automation, Chongqing University, ChongQing 400044

2.School of Mathematics, Anhui University, Hefei 230039

*Correspondence author

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Funding: the Specialized Research Fund for the Doctoral Program of Higher Education of China（No.No.200806110021）, the Natural Science Foundation of Anhui Province（No.No.11040606M12）, the Natural Science Foundation of Anhui Education Bureau（No.No.KJ2010A035）, the National Natural Science Foundation of China （No.No.60974090）

Opened online:21 January 2012

Accepted by: none

Citation: CHEN Liping,CHAI Yi,WU Ranchao.Cluster synchronization in fractional-order complex dynamical networks[OL]. [21 January 2012] http://en.paper.edu.cn/en_releasepaper/content/4461562

Cluster synchronization of complex dynamical networks with fractional-order dynamical nodes is discussed in the paper. By using the stability theory of fractional-order differential system and linear pinning control, a sufficient condition for the stability of the synchronization behavior in complex networks with fractional order dynamics is derived. Only the nodes in one community which have direct connections to the nodes in other communities are needed to be controlled, resulting in reduced control cost. A numerical example is presented to demonstrate the validity and feasibility of the obtained result. Numerical simulations illustrate that cluster synchronization performance for fractional-order complex dynamical networks is influenced by inner-coupling matrix, control gain, coupling strength and topological structures of the networks.

Keywords:Cluster synchronization; Complex dynamical networks; Fractional-order; Pinning control

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