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Title: Drive network to a desired orbit by pinning control (English)
Author: Wu, Quanjun
Author: Zhang, Hua
Language: English
Journal: Kybernetika
ISSN: 0023-5954 (print)
ISSN: 1805-949X (online)
Volume: 51
Issue: 1
Year: 2015
Pages: 150-172
Summary lang: English
Category: math
Summary: The primary objective of the present paper is to develop an approach for analyzing pinning synchronization stability in a complex delayed dynamical network with directed coupling. Some simple yet generic criteria for pinning such coupled network are derived analytically. Compared with some existing works, the primary contribution is that the synchronization manifold could be chosen as a weighted average of all the nodes states in the network for the sake of practical control tactics, which displays the different influences and contributions of the various nodes in synchronization seeking processes of the dynamical network. Furthermore, it is shown that in order to drive a complex network to a desired synchronization state, the coupling strength should vary according to the controller. In addition, the theoretical results about the time-invariant network is extended to the time-varying network, and the result on synchronization problem can also be extended to the consensus problem of networked multi-agent systems. Subsequently, the theoretic results are illustrated by a typical scale-free (SF) neuronal network. Numerical simulations with three kinds of the homogenous solutions, including an equilibrium point, a periodic orbit, and a chaotic attractor, are finally given to demonstrate the effectiveness of the proposed control methodology. (English)
Keyword: complex dynamical network
Keyword: pinning control
Keyword: directed coupling
Keyword: time delay
Keyword: DCN oscillator
MSC: 34D06
MSC: 34K20
MSC: 70K40
MSC: 74H65
idZBL: Zbl 06433837
idMR: MR3333838
DOI: 10.14736/kyb-2015-1-0150
Date available: 2015-03-23T18:58:34Z
Last updated: 2016-01-03
Stable URL:
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