Top

Neural Processing Letters

Published in:

01-06-2018

Invariant and Attracting Sets of Complex-Valued Neural Networks with Both Time-Varying and Infinite Distributed Delays

Authors: Zhao Yang, Xiaofeng Liao

Published in: Neural Processing Letters | Issue 3/2019

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

In this paper, we investigate the asymptotic property of non-autonomous complex-valued neural networks with time-varying delays and infinite distributed delays. By using the property of M-matrix, an integro-differential inequality is established. Based on the inequality and some sufficient conditions, we obtain the attracting and invariant sets of non-autonomous complex-valued neural networks with time-varying delays and infinite distributed delays. An example with numerical simulation is given out to illustrate the effectiveness of our results.

previous article Convergence of Neutral Type Fuzzy Cellular Neural Networks with D Operator

next article Anti-periodic Solutions for Quaternion-Valued High-Order Hopfield Neural Networks with Time-Varying Delays

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Hirose A (2003) Complex-valued neural networks: theories and applications. World Scientific, SingaporeCrossRefMATH

Bohner M, Sanyal S (2011) Global fof complex-valued neural networks on time case. Differ Equ Dyn Syst 19:3–11MathSciNetCrossRef

Liu X, Fang K, Liu B (2009) A synthesis method based on stability analysis for complex-valued Hopfield neural network. In: Proceedings of the 7th Asian control conference, pp 1245–1250

Hirose A (2010) Recent progress in applications of complex-valued neural networks. In: Proceedings of 10th international conference on artificiality intelligence soft computing, pp 42–46

Song QK, Yan H, Zhao ZJ, Liu YR (2016) Global exponential stability of complex-valued neural networks with both time-varying delays and impulsive effects. Neural Netw 79:108–116CrossRef

Hu J, Wang J (2012) Global stability of complex-valued recurrent neural networks with time-delays. IEEE Trans Neural Netw Learn Syst 23:853–865CrossRef

Zhou B, Song QK (2013) Boundedness and complete stability of complex-valued neural networks with time delay. IEEE Trans Neural Netw Learn Syst 24:1227–1238CrossRef

Velmurugan G, Rakkiyappan R, Cao JD (2015) Further analysis of global \(\mu \)-stability of complex-valued neural networks with unbounded time-varying delays. Neural Netw 67:14–27CrossRefMATH

Pan J, Liu XZ (2015) Exponential stability of a class of complex-valued neural networks with time-varying delays. Neurocomputing 164:293–299CrossRef

10.

Fang T, Sun J (2014) Further investigate the stability of complex-valued recurrent neural networks with time-delays. IEEE Trans Neural Netw Learn Syst 25:1709–1713CrossRef

11.

Rakkiyappan R, Velmurugan G, Li XD (2015) Complete stability analysis of complex-valued neural networks with time delays and impulses. Neural Process Lett 41:435–468CrossRefMATH

12.

Xu LG, Xu DY (2008) Exponential stability of nonlinear impulsive neutral integro-differential equation. Nonlinear Anal 69:2910–2923MathSciNetCrossRefMATH

13.

Zhang Z, Chen B (2014) Global stability criterion for delayed complex-valued recurrent neural networks. IEEE Trans Neural Netw Learn Syst 25:1704–1708CrossRef

14.

Liao XX, Luo Q, Zeng ZG (1994) Positive invariant and global exponential attractive sets of neural networks with time-varying delays. Neurocomputing 71:513–518CrossRef

15.

Liao XF, Luo Q, Zeng ZG (2008) Positive invariant and global exponential attractive sets of neural networks with time-varying delays. Neurocomputing 71:513–518CrossRef

16.

Xu DY, Yang ZC (2007) Attracting and invariant sets for a class of impulsive functional differential equations. J Math Anal Appl 329:1036–1044MathSciNetCrossRefMATH

17.

Zhao ZH, Jian JG (2014) Attracting and quasi-invariant sets for BAM neural networks of neutral-type with time-varying and infinite distributed delays. Neurocomputing 140:265–272CrossRef

18.

Li YP, Liao XF (2016) Global attracting sets of non-autonomous and complex-valued neural networks with time-varying delays. Neurocomputing 173:994–1000CrossRef

19.

Zhao ZH, Jian JG, Wang BX (2015) Global attracting sets for neutral-type BAM neural networks with time-varying and infinite distributed delays. Nonliner Anal Hybrid Syst 15:63–73MathSciNetCrossRefMATH

20.

Teng LY, Xu DY (2012) Global attracting set for non-autonomous neutral type neural networks with distributed delays. Neurocomputing 94:64–67CrossRef

21.

Huang YM, Zhu W, Xu DY (2009) Invariant and attracting set of fuzzy cellular neural networks with variable delays. Appl Math Lett 22:478–483MathSciNetCrossRefMATH

22.

Song QK, Cao JD (2009) Stability analysis of Cohen–Grossberg neural network with both time-varying and continuously distributed delays. J Comput Appl Math 197:188–203MathSciNetCrossRefMATH

23.

Rakkiyappan R, Velmurugan G, Cao JD (2016) Multiple \(\mu \)-stability analysis of complex-valued neural networks with unbounded time-varying delays. Neurocomputing 173:2083–2089CrossRef

24.

Wu B, Liu Y, Lu JQ (2012) New results on global exponential stability for impulsive cellular neural networks with any bounded time-varying delays. Math Comput Model 55:837–843MathSciNetCrossRefMATH

25.

Liu Y, Zhang DD, Lu JQ, Cao JD (2016) Global \(\mu \)-stability criteria for quaternion-valued neural networks with unbounded time-varying delays. Inf Sci 360:273–288CrossRef

26.

Jian JG, Wang B (2015) Stability analysis in Lagrange sense for a class of BAM neural networks of neutral type with multiple time-varying delays. Neurocomputing 149:930–939CrossRef

27.

Zhu JW, Sun J (2016) Global exponential stability of Clifford-valued recurrent neural networks. Neurocomputing 173:685–689CrossRef

28.

Wang B, Jian JG, Guo CD (2008) Global exponential stability of a class of BAM networks with time-varying delays and continuously distributed delays. Neurocomputing 71:495–501CrossRef

29.

Liao XF, Luo Q, Zhang W (2006) Delay-dependent asymptotic stability for neural networks with distributed delays. Nonlinear Anal 7:1178–1192MathSciNetCrossRefMATH

30.

Horn RA, Johnson CR (1985) Matrix analysis. Cambridge University Press, CambridgeCrossRefMATH

31.

Liu Y, Xu P, Lu JQ, Liang JL (2016) Global stability of Clifford-valued recurrent neural networks with time delay. Nonlinear Dyn 84:767–777MathSciNetCrossRefMATH

Title: Invariant and Attracting Sets of Complex-Valued Neural Networks with Both Time-Varying and Infinite Distributed Delays
Authors: Zhao Yang
Xiaofeng Liao
Publication date: 01-06-2018
Publisher: Springer US
Published in: Neural Processing Letters / Issue 3/2019
Print ISSN: 1370-4621
Electronic ISSN: 1573-773X
DOI: https://doi.org/10.1007/s11063-018-9848-y

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Other articles of this Issue 3/2019

Complex Fuzzy Concept Lattice

Obstacle Detection by Fusing Point Clouds and Monocular Image

Discriminative Autoencoder for Feature Extraction: Application to Character Recognition

An Improved Method for Semantic Image Inpainting with GANs: Progressive Inpainting

Discriminative Probabilistic Latent Semantic Analysis with Application to Single Sample Face Recognition

Pseudo Almost Automorphic Solutions for Multidirectional Associative Memory Neural Network with Mixed Delays