Adaptive Modified Function Projective Synchronization of Uncertain Complex Dynamical Networks with Multiple Time-Delay Couplings and Disturbances

Adaptive Modified Function Projective Synchronization of Uncertain Complex Dynamical Networks with Multiple Time-Delay Couplings and Disturbances

This paper studies the modified function projective synchronization of uncertain complex dynamic network model with multiple time-delay couplings and external disturbances. Based on Lyapunov stability theory, the positive definite function is designed and the sufficient conditions of synchronization...

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Main Authors: Jie Fang, Na Liu, Junwei Sun
Format: Article
Language:English
Published: Hindawi Limited 2018-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2018/6384757
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spelling doaj-d9d8bd05595c4d4696dcfd61f23c53872020-11-24T21:01:15ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472018-01-01201810.1155/2018/63847576384757Adaptive Modified Function Projective Synchronization of Uncertain Complex Dynamical Networks with Multiple Time-Delay Couplings and DisturbancesJie Fang0Na Liu1Junwei Sun2College of Electric and Information Engineering, Zhengzhou University of Light Industry, Zhengzhou 450002, ChinaCollege of Electric and Information Engineering, Zhengzhou University of Light Industry, Zhengzhou 450002, ChinaCollege of Electric and Information Engineering, Zhengzhou University of Light Industry, Zhengzhou 450002, ChinaThis paper studies the modified function projective synchronization of uncertain complex dynamic network model with multiple time-delay couplings and external disturbances. Based on Lyapunov stability theory, the positive definite function is designed and the sufficient conditions of synchronization are given. Both the uncertain parameters and the unknown bounded disturbances are estimated in accordance with the adaptive laws. With the adaptive feedback controller, the complex dynamic network can synchronize with reference node by a scaling function matrix. The reference node can be periodic orbit, equilibrium point, or a chaotic attractor. Finally, two numerical simulations are offered to illustrate the effectiveness of the proposed method.http://dx.doi.org/10.1155/2018/6384757
collection DOAJ
language English
format Article
sources DOAJ
author Jie Fang
Na Liu
Junwei Sun
spellingShingle Jie Fang
Na Liu
Junwei Sun
Adaptive Modified Function Projective Synchronization of Uncertain Complex Dynamical Networks with Multiple Time-Delay Couplings and Disturbances
Mathematical Problems in Engineering
author_facet Jie Fang
Na Liu
Junwei Sun
author_sort Jie Fang
title Adaptive Modified Function Projective Synchronization of Uncertain Complex Dynamical Networks with Multiple Time-Delay Couplings and Disturbances
title_short Adaptive Modified Function Projective Synchronization of Uncertain Complex Dynamical Networks with Multiple Time-Delay Couplings and Disturbances
title_full Adaptive Modified Function Projective Synchronization of Uncertain Complex Dynamical Networks with Multiple Time-Delay Couplings and Disturbances
title_fullStr Adaptive Modified Function Projective Synchronization of Uncertain Complex Dynamical Networks with Multiple Time-Delay Couplings and Disturbances
title_full_unstemmed Adaptive Modified Function Projective Synchronization of Uncertain Complex Dynamical Networks with Multiple Time-Delay Couplings and Disturbances
title_sort adaptive modified function projective synchronization of uncertain complex dynamical networks with multiple time-delay couplings and disturbances
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2018-01-01
description This paper studies the modified function projective synchronization of uncertain complex dynamic network model with multiple time-delay couplings and external disturbances. Based on Lyapunov stability theory, the positive definite function is designed and the sufficient conditions of synchronization are given. Both the uncertain parameters and the unknown bounded disturbances are estimated in accordance with the adaptive laws. With the adaptive feedback controller, the complex dynamic network can synchronize with reference node by a scaling function matrix. The reference node can be periodic orbit, equilibrium point, or a chaotic attractor. Finally, two numerical simulations are offered to illustrate the effectiveness of the proposed method.
url http://dx.doi.org/10.1155/2018/6384757
work_keys_str_mv AT jiefang adaptivemodifiedfunctionprojectivesynchronizationofuncertaincomplexdynamicalnetworkswithmultipletimedelaycouplingsanddisturbances
AT naliu adaptivemodifiedfunctionprojectivesynchronizationofuncertaincomplexdynamicalnetworkswithmultipletimedelaycouplingsanddisturbances
AT junweisun adaptivemodifiedfunctionprojectivesynchronizationofuncertaincomplexdynamicalnetworkswithmultipletimedelaycouplingsanddisturbances
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