Dynamics Analysis of a New Fractional-Order Hopfield Neural Network with Delay and Its Generalized Projective Synchronization

Dynamics Analysis of a New Fractional-Order Hopfield Neural Network with Delay and Its Generalized Projective Synchronization

In this paper, a new three-dimensional fractional-order Hopfield-type neural network with delay is proposed. The system has a unique equilibrium point at the origin, which is a saddle point with index two, hence unstable. Intermittent chaos is found in this system. The complex dynamics are analyzed...

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Main Authors: Han-Ping Hu, Jia-Kun Wang, Fei-Long Xie
Format: Article
Language:English
Published: MDPI AG 2018-12-01
Series:Entropy
Subjects:
dynamics analysis
fractional-order
Hopfield neural network
generalized projective synchronization
Online Access:https://www.mdpi.com/1099-4300/21/1/1
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spelling doaj-cb061638c6f4484fac05745e6a090fff2020-11-24T21:49:13ZengMDPI AGEntropy1099-43002018-12-01211110.3390/e21010001e21010001Dynamics Analysis of a New Fractional-Order Hopfield Neural Network with Delay and Its Generalized Projective SynchronizationHan-Ping Hu0Jia-Kun Wang1Fei-Long Xie2School of Automation, Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan 430074, ChinaSchool of Automation, Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan 430074, ChinaSchool of Automation, Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan 430074, ChinaIn this paper, a new three-dimensional fractional-order Hopfield-type neural network with delay is proposed. The system has a unique equilibrium point at the origin, which is a saddle point with index two, hence unstable. Intermittent chaos is found in this system. The complex dynamics are analyzed both theoretically and numerically, including intermittent chaos, periodicity, and stability. Those phenomena are confirmed by phase portraits, bifurcation diagrams, and the Largest Lyapunov exponent. Furthermore, a synchronization method based on the state observer is proposed to synchronize a class of time-delayed fractional-order Hopfield-type neural networks.https://www.mdpi.com/1099-4300/21/1/1dynamics analysisfractional-orderHopfield neural networkgeneralized projective synchronization
collection DOAJ
language English
format Article
sources DOAJ
author Han-Ping Hu
Jia-Kun Wang
Fei-Long Xie
spellingShingle Han-Ping Hu
Jia-Kun Wang
Fei-Long Xie
Dynamics Analysis of a New Fractional-Order Hopfield Neural Network with Delay and Its Generalized Projective Synchronization
Entropy
dynamics analysis
fractional-order
Hopfield neural network
generalized projective synchronization
author_facet Han-Ping Hu
Jia-Kun Wang
Fei-Long Xie
author_sort Han-Ping Hu
title Dynamics Analysis of a New Fractional-Order Hopfield Neural Network with Delay and Its Generalized Projective Synchronization
title_short Dynamics Analysis of a New Fractional-Order Hopfield Neural Network with Delay and Its Generalized Projective Synchronization
title_full Dynamics Analysis of a New Fractional-Order Hopfield Neural Network with Delay and Its Generalized Projective Synchronization
title_fullStr Dynamics Analysis of a New Fractional-Order Hopfield Neural Network with Delay and Its Generalized Projective Synchronization
title_full_unstemmed Dynamics Analysis of a New Fractional-Order Hopfield Neural Network with Delay and Its Generalized Projective Synchronization
title_sort dynamics analysis of a new fractional-order hopfield neural network with delay and its generalized projective synchronization
publisher MDPI AG
series Entropy
issn 1099-4300
publishDate 2018-12-01
description In this paper, a new three-dimensional fractional-order Hopfield-type neural network with delay is proposed. The system has a unique equilibrium point at the origin, which is a saddle point with index two, hence unstable. Intermittent chaos is found in this system. The complex dynamics are analyzed both theoretically and numerically, including intermittent chaos, periodicity, and stability. Those phenomena are confirmed by phase portraits, bifurcation diagrams, and the Largest Lyapunov exponent. Furthermore, a synchronization method based on the state observer is proposed to synchronize a class of time-delayed fractional-order Hopfield-type neural networks.
topic dynamics analysis
fractional-order
Hopfield neural network
generalized projective synchronization
url https://www.mdpi.com/1099-4300/21/1/1
work_keys_str_mv AT hanpinghu dynamicsanalysisofanewfractionalorderhopfieldneuralnetworkwithdelayanditsgeneralizedprojectivesynchronization
AT jiakunwang dynamicsanalysisofanewfractionalorderhopfieldneuralnetworkwithdelayanditsgeneralizedprojectivesynchronization
AT feilongxie dynamicsanalysisofanewfractionalorderhopfieldneuralnetworkwithdelayanditsgeneralizedprojectivesynchronization
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