A graph approach to synchronization in complex networks of asymmetrically nonlinear coupled dynamical systems

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/51175

Title:	A graph approach to synchronization in complex networks of asymmetrically nonlinear coupled dynamical systems
Authors:	Li,CH;Yang,SY
Contributors:	數學系
Keywords:	HINDMARSH-ROSE NEURONS;CHAOTIC SYSTEMS;EXPONENTIAL SYNCHRONIZATION;NEURAL-NETWORKS;OSCILLATORS;ARRAYS;MODEL
Date:	2011
Issue Date:	2012-03-27 18:24:06 (UTC+8)
Publisher:	國立中央大學
Abstract:	In this paper, we investigate the global exponential synchronization in complex networks of nonlinearly coupled dynamical systems with an asymmetric outer-coupling matrix. Employing the Lyapunov function approach with some graph theory techniques, we improve the so-called connection graph stability method for the synchronization analysis, that was originally developed by Belykh et al. for symmetrically linear coupled dynamical systems, to fit the asymmetrically nonlinear coupled case. We derive some criteria that ensure the nonlinearly coupled as well as linearly coupled dynamical systems to be globally exponentially synchronized. An illustrative example of a regular network with a modular structure of nonlinearly coupled Hindmarsh-Rose neurons is provided. We further consider a small-world dynamical network of nonlinearly coupled Chua's circuits and demonstrate both theoretically and numerically that the small-world dynamical network is easier to synchronize than the original regular dynamical network. More interestingly, numerical results of a real-world network of the cat cortex modelled by the asymmetrically linear coupled FitzHugh-Nagumo equations are also presented.
Relation:	JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
Appears in Collections:	[Department of Mathematics] journal & Dissertation

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