Exponential synchronization of the complex dynamical networks with a coupling delay and impulsive effects
type: Item
instance of: scholarly article
title: Exponential synchronization of the complex dynamical networks with a coupling delay and impulsive effects
zbMATH Open document ID: 1204.34072
author: Yongqing Yang
author: Jinde Cao
published in: Nonlinear Analysis. Real World Applications
publication date: 2010-06-03T00:00:00Z
review text: For a class of complex networks of interacting identical dynamical systems with impulsive effects, a problem of synchronization is studied. The coupling in the networks is considered to be with a time delay such that each element of the ensemble receives retarded signals from other oscillators. The coupling matrix belongs to a class of irreducible matrices with zero row sums and non-negative elements except for the main diagonal. Under further assumptions on the vector fields of the interacting oscillators and the coupling matrix, exponential stability of the synchronized manifold is demonstrated. The latter means that the synchronization errors decay to zero exponentially fast with time. Sufficient conditions for the exponential synchronization are derived by the geometrical decomposition of the network states over the eigenvectors of the coupling matrix and linear matrix inequality methods. Two numerical examples are also presented to illustrate the applicability of the obtained analytical results.
Mathematics Subject Classification ID: 34D06
Mathematics Subject Classification ID: 34A37
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K25
zbMATH DE Number: 5716735
zbMATH Keywords: exponential synchronization
zbMATH Keywords: complex network
zbMATH Keywords: impulsive effect
zbMATH Keywords: delay
reviewed by: Oleksandr Popovych
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2009.03.020
OpenAlex ID: W2049369191
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DOI: 10.1016/J.NONRWA.2009.03.020
description: scientific article; zbMATH DE number 5716735