Adaptive cluster synchronization in networks with time-varying and distributed coupling delays

K. Li, J. Zhou, W. Yu, Michael Small, X. Fu

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

This paper studies the adaptive cluster synchronization of a generalized linearly coupled network with time-varying delay and distributed delays. This network includes nonidentical nodes displaying different local dynamical behaviors, while for each cluster of that network the internal dynamics is uniform (such as chaotic, periodic, or stable behavior). In particular, the generalized coupling matrix of this network can be asymmetric and weighted. Two different adaptive laws of time-varying coupling strength and a linear feedback control are designed to achieve the cluster synchronization of this network. Some sufficient conditions to ensure the cluster synchronization are obtained by using the invariant principle of functional differential equations and linear matrix inequality (LMI). Numerical simulations verify the efficiency of our proposed adaptive control method. © 2013 Elsevier Inc.
Original languageEnglish
Pages (from-to)1300-1314
JournalApplied Mathematical Modelling
Volume38
Issue number4
DOIs
Publication statusPublished - 2014

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Time-varying
Synchronization
Linear matrix inequalities
Feedback control
Differential equations
Linear Control
Distributed Delay
Time-varying Delay
Functional Differential Equations
Dynamical Behavior
Adaptive Control
Feedback Control
Computer simulation
Matrix Inequality
Linear Inequalities
Linearly
Verify
Internal
Numerical Simulation
Invariant

Cite this

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title = "Adaptive cluster synchronization in networks with time-varying and distributed coupling delays",
abstract = "This paper studies the adaptive cluster synchronization of a generalized linearly coupled network with time-varying delay and distributed delays. This network includes nonidentical nodes displaying different local dynamical behaviors, while for each cluster of that network the internal dynamics is uniform (such as chaotic, periodic, or stable behavior). In particular, the generalized coupling matrix of this network can be asymmetric and weighted. Two different adaptive laws of time-varying coupling strength and a linear feedback control are designed to achieve the cluster synchronization of this network. Some sufficient conditions to ensure the cluster synchronization are obtained by using the invariant principle of functional differential equations and linear matrix inequality (LMI). Numerical simulations verify the efficiency of our proposed adaptive control method. {\circledC} 2013 Elsevier Inc.",
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Adaptive cluster synchronization in networks with time-varying and distributed coupling delays. / Li, K.; Zhou, J.; Yu, W.; Small, Michael; Fu, X.

In: Applied Mathematical Modelling, Vol. 38, No. 4, 2014, p. 1300-1314.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Adaptive cluster synchronization in networks with time-varying and distributed coupling delays

AU - Li, K.

AU - Zhou, J.

AU - Yu, W.

AU - Small, Michael

AU - Fu, X.

PY - 2014

Y1 - 2014

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AB - This paper studies the adaptive cluster synchronization of a generalized linearly coupled network with time-varying delay and distributed delays. This network includes nonidentical nodes displaying different local dynamical behaviors, while for each cluster of that network the internal dynamics is uniform (such as chaotic, periodic, or stable behavior). In particular, the generalized coupling matrix of this network can be asymmetric and weighted. Two different adaptive laws of time-varying coupling strength and a linear feedback control are designed to achieve the cluster synchronization of this network. Some sufficient conditions to ensure the cluster synchronization are obtained by using the invariant principle of functional differential equations and linear matrix inequality (LMI). Numerical simulations verify the efficiency of our proposed adaptive control method. © 2013 Elsevier Inc.

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