Mathematical Model and Cluster Synchronization for a Complex Dynamical Network with Two Types of Chaotic Oscillators

We propose a mathematical model of a complex dynamical network consisting of two types of chaotic oscillators and investigate the schemes and corresponding criteria for cluster synchronization. The global asymptotically stable criteria for the linearly or adaptively coupled network are derived to en...

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Main Authors: Zhen Jia, Guangming Deng
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2012/595360
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author Zhen Jia
Guangming Deng
author_facet Zhen Jia
Guangming Deng
author_sort Zhen Jia
collection DOAJ
description We propose a mathematical model of a complex dynamical network consisting of two types of chaotic oscillators and investigate the schemes and corresponding criteria for cluster synchronization. The global asymptotically stable criteria for the linearly or adaptively coupled network are derived to ensure that each group of oscillators is synchronized to the same behavior. The cluster synchronization can be guaranteed by increasing the inner coupling strength in each cluster or enhancing the external excitation. Theoretical analysis and numerical simulation results show that the external excitation is more conducive to the cluster synchronization. All of the results are proved rigorously. Finally, a network with a scale-free subnetwork and a small-world subnetwork is illustrated, and the corresponding numerical simulations verify the theoretical analysis.
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issn 1110-757X
1687-0042
language English
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series Journal of Applied Mathematics
spelling doaj-art-2fdebb7d1ab04b869ea14cabcf2110012025-08-20T03:20:22ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/595360595360Mathematical Model and Cluster Synchronization for a Complex Dynamical Network with Two Types of Chaotic OscillatorsZhen Jia0Guangming Deng1College of Science, Guilin University of Technology, Guilin 541004, ChinaCollege of Science, Guilin University of Technology, Guilin 541004, ChinaWe propose a mathematical model of a complex dynamical network consisting of two types of chaotic oscillators and investigate the schemes and corresponding criteria for cluster synchronization. The global asymptotically stable criteria for the linearly or adaptively coupled network are derived to ensure that each group of oscillators is synchronized to the same behavior. The cluster synchronization can be guaranteed by increasing the inner coupling strength in each cluster or enhancing the external excitation. Theoretical analysis and numerical simulation results show that the external excitation is more conducive to the cluster synchronization. All of the results are proved rigorously. Finally, a network with a scale-free subnetwork and a small-world subnetwork is illustrated, and the corresponding numerical simulations verify the theoretical analysis.http://dx.doi.org/10.1155/2012/595360
spellingShingle Zhen Jia
Guangming Deng
Mathematical Model and Cluster Synchronization for a Complex Dynamical Network with Two Types of Chaotic Oscillators
Journal of Applied Mathematics
title Mathematical Model and Cluster Synchronization for a Complex Dynamical Network with Two Types of Chaotic Oscillators
title_full Mathematical Model and Cluster Synchronization for a Complex Dynamical Network with Two Types of Chaotic Oscillators
title_fullStr Mathematical Model and Cluster Synchronization for a Complex Dynamical Network with Two Types of Chaotic Oscillators
title_full_unstemmed Mathematical Model and Cluster Synchronization for a Complex Dynamical Network with Two Types of Chaotic Oscillators
title_short Mathematical Model and Cluster Synchronization for a Complex Dynamical Network with Two Types of Chaotic Oscillators
title_sort mathematical model and cluster synchronization for a complex dynamical network with two types of chaotic oscillators
url http://dx.doi.org/10.1155/2012/595360
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AT guangmingdeng mathematicalmodelandclustersynchronizationforacomplexdynamicalnetworkwithtwotypesofchaoticoscillators