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Complex network; the pinning synchronization; synchronizability.

It is proved that the maximum eigenvalue sequence of the principal submatrices of coupling matrix is decreasing. The method of calculating the number of pinning nodes is given based on this theory. The findings reveal the relationship between the decreasing speed of maximum eigenvalue sequence of the principal submatrices for coupling matrix and the synchronizability on complex networks via pinning control. We discuss the synchronizability on some networks, such as scale-free networks and small-world networks. Numerical simulations show that different pinning strategies have different pinning synchronizability on the same complex network, and the synchronizability with pinning control is consistent with one without pinning control in various complex networks.

Yi Liang^{1 2} Xingyuan Wang¹

1. Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024, China
2. Department of Electronics and Information Engineering, Yili Normal College, Yining 835000, China

Published

April 2013

Manuscript received

18 January 2012

Manuscript revised

14 August 2012

Accepted

8 October 2012