Taiwanese Journal of Mathematics

ESTIMATION OF DELAY ON SYNCHRONIZATION STABILITY IN A CLASS OF COMPLEX SYSTEMS WITH COUPLING DELAYS

Zhisheng Duan, Qingyun Wang, Zhaosheng Feng, and Guanrong Chen

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Abstract

Nowadays one of the most concerned topics in the field of complex networks is to find how the synchronizability depends on various parameters of networks. Complex networks with coupling delays have gained increasing attention in various fields of science and engineering in the past decade. One interesting problem is to investigate the effect of delay on dynamical behaviors and to determine the range of delay, in which, the synchronization stability can be achieved. In this paper, based on the qualitative theory of linear time-delay systems, the synchronization stability in complex dynamical networks with coupling delays is considered and some stability criteria of synchronization state are obtained. It is shown that by virtue of these obtained criteria, the range of delay on synchronization stability of complex networks with coupling delays can be analytically estimated. Finally, a couple of examples are illustrated which agree well with our theoretical results.

Article information

Source
Taiwanese J. Math., Volume 12, Number 8 (2008), 2141-2154.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405140

Digital Object Identifier
doi:10.11650/twjm/1500405140

Mathematical Reviews number (MathSciNet)
MR2459818

Zentralblatt MATH identifier
1179.34082

Subjects
Primary: 34D30: Structural stability and analogous concepts [See also 37C20] 37N25: Dynamical systems in biology [See mainly 92-XX, but also 91-XX]

Keywords
complex networks coupling delays estimate asymptotic stability synchronization stability

Citation

Duan, Zhisheng; Wang, Qingyun; Feng, Zhaosheng; Chen, Guanrong. ESTIMATION OF DELAY ON SYNCHRONIZATION STABILITY IN A CLASS OF COMPLEX SYSTEMS WITH COUPLING DELAYS. Taiwanese J. Math. 12 (2008), no. 8, 2141--2154. doi:10.11650/twjm/1500405140. https://projecteuclid.org/euclid.twjm/1500405140


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