Abstract and Applied Analysis

Criterion for Unbounded Synchronous Region in Complex Networks

Jin Zhou

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Abstract

Synchronization of complex networks has been extensively studied in many fields, where intensive efforts have been devoted to the understanding of its mechanisms. As for discriminating network synchronizability by Master Stability Function method, a dilemma usually encountered is that we have no prior knowledge of the network type that the synchronous region belongs to. In this paper, we investigate a sufficient condition for a general complex dynamical network in the absence of control. A main result is that, when the coupling strength is sufficiently strong, the dynamical network achieves synchronization provided that the symmetric part of the inner-coupling matrix is positive definite. According to our results, synchronous region of the network with positive definite inner-coupling matrix belongs to the unbounded one, and then the eigenvalue of the outer-coupling matrix nearest 0 can be used for judging synchronizability. Even though we cannot gain the necessary and sufficient conditions for synchronizing a network so far, our results constitute a first step toward a better understanding of network synchronization.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 513871, 8 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393449810

Digital Object Identifier
doi:10.1155/2013/513871

Mathematical Reviews number (MathSciNet)
MR3121533

Zentralblatt MATH identifier
1291.34090

Citation

Zhou, Jin. Criterion for Unbounded Synchronous Region in Complex Networks. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 513871, 8 pages. doi:10.1155/2013/513871. https://projecteuclid.org/euclid.aaa/1393449810


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