Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Neural Processing Letters
Published in: Neural Processing Letters 2/2015

01-10-2015

Stability Analysis of Fractional-Order Neural Networks with Time Delay

Authors: Hu Wang, Yongguang Yu, Guoguang Wen, Shuo Zhang

Published in: Neural Processing Letters | Issue 2/2015

Log in

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

search-config
loading …

Abstract

The stability analysis of fractional-order Hopfield neural networks with time delay is investigated. A stability theorem of fractional-order neural networks with time delay is derived. The stability conditions of the two-dimensional fractional-order neural networks with time delay are obtained. Furthermore, the three-dimensional fractional-order neural networks with different ring structures and time delay are proposed, and their stability conditions are derived. To illustrate the effectiveness of our theoretical results, numerical examples and simulations are also presented.
previous article An Effective Neural Learning Algorithm for Extracting Cross-Correlation Feature Between Two High-Dimensional Data Streams
next article Synchronization Analysis of Coupled Stochastic Neural Networks with On–Off Coupling and Time-Delay

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
Literature
1.
2.
Koeller RC (1986) Polynomial operators, stieltjes convolution, and fractional calculus in hereditary mechanics. Acta Mech 58:251–264MathSciNetCrossRefMATH
3.
Heaviside O (1971) Electromagnetic theory. Chelsea, New York
4.
Podlubny I (1999) Fractional differential equations. Academic Press, New York
5.
Shantanu D (2011) Functional fractional calculus. Springer, Berlin
6.
Li Y, Chen YQ, Podlubny I (2009) Mittag–Leffler stability of fractional order nonlinear dynamic systems. Automatica 45(8):1965–1969MathSciNetCrossRefMATH
7.
8.
Zhang FR, Li CP, Chen YQ (2011) Asymptotical stability of nonlinear fractional differential system with Caputo derivative. Int J Differ Equ, p 635165
9.
Hadi D, Dumitru B, Jalil S (2012) Stability analysis of Caputo fractional-order nonlinear systems revisited. Nonlinear Dyn 67:2433–2439CrossRef
10.
Yu JM, Hu H, Zhou SB, Lin XR (2013) Generalized Mittag–Leffler stability of multi-variables fractional order nonlinear systems. Automatica 49:1798–1803MathSciNetCrossRefMATH
11.
Bonnet C, Partington JR (2002) Analysis of fractional delay systems of retarded and neutral type. Automatica 38:1133–1138MathSciNetCrossRef
12.
Wang CH, Cheng YC (2006) A numerical algorithm for stability testing of fractional delay systems. Automatica 42:825–831CrossRefMATH
13.
Yang ZH, Cao JD (2013) Initial value problems for arbitrary order fractional differential equations with delay. Commun Nonlinear Sci Numer Simul 18:2993–3005MathSciNetCrossRef
14.
Deng WH, Li CP, Lü JH (2007) Stability analysis of linear fractional differential system with multiple time delays. Nonlinear Dyn 48(4):409–416CrossRefMATH
15.
Lazarević M, Spasi A (2009) Finite-time stability analysis of fractional order time delay systems: Gronwall’s approach. Math Comput Model 49:475–481CrossRef
16.
Afshin M, Mohammad H (2013) Stability of linear time invariant fractional delay systems of retarded type in the space of delay parameters. Automatica 49:1287–1294CrossRef
17.
Hopfield J (1984) Neurons with graded response have collective computational properties like those of two-state neurons. Proc Natl Acad Sci USA 81:3088–3092CrossRef
18.
Wang JL, Wu HN, Guo L (2011) Passivity and stability analysis of reaction-diffusion neural networks with dirichlet boundary conditions. IEEE Trans Neural Netw 22(12):2105–2116CrossRef
19.
Wang JL, Wu HN, Guo L (2013) Stability analysis of reaction-diffusion Cohen–Grossberg neural networks under impulsive control. Neurocomput 106:21–30MathSciNetCrossRef
20.
Kao YG, Wang CH, Zhang L (2013) Delay-dependent robust exponential stability of impulsive markovian jumping reaction-diffusion Cohen–Grossberg neural networks. Neural Process Lett 38(3):321–346CrossRef
21.
Arik S (2004) An analysis of exponential stability of delayed neural networks with time varying delays. Neural Netw 17:1027–1031CrossRef
22.
Mou S, Gao H, Qiang W, Chen K (2008) New delay-dependent exponetial stability for neural networks with time delay. IEEE Trans Syst Man Cybern B Cybern 38(2):571–576CrossRef
23.
Hu C, Jiang HJ, Teng ZD (2010) Globally exponential stability for delayed neural networks under impulsive control. Neural Process Lett 31(2):105–127CrossRef
24.
Chandran R, Balasubramaniam P (2013) Delay dependent exponential stability for fuzzy recurrent neural networks with interval time-varying delay. Neural Process Lett 37(2):147–161CrossRef
25.
Wang JL, Wu HN (2011) Stability analysis of impulsive parabolic complex networks. Chaos Soliton Fract 44(11):1020–1034CrossRef
26.
Yu WW, Cao JD, Chen GR (2008) Stability and Hopf bifurcation of a general delayed recurrent nrural network. IEEE Trans Neural Netw 19(5):845–854CrossRefMATH
27.
Jiang F, Shen Y (2013) Stability of stochastic \(\theta \)-methods for stochastic delay Hopfield neural networks under regime switching. Neural Process Lett 38(3):433–444MathSciNetCrossRefMATH
28.
Lundstrom B, Higgs M, Spain W, Fairhall A (2008) Fractional differentiation by neocortical pyramidal neurons. Nat Neurosci 11:1335–1342CrossRefMATH
29.
Kaslik E, Sivasundaram S (2011) Dynamics of fractional-order neural networks. In: Proceedings of the international conference on neural networks. California, USA, IEEE, pp 611–618
30.
Kaslik E, Sivasundaram S (2012) Nonlinear dynamics and chaos in fractional-order neural networks. Neural Netw 32:245–256CrossRef
31.
Boroomand A, Menhaj M (2009) Fractional-order Hopfield neural networks. Lect Notes Comput Sci 5506:883–890CrossRef
32.
Arena P, Fortuna L, Porto D (2000) Chaotic behavior in nonintegerorder cellular neural networks. Phys Rev E 61:777–781CrossRefMATH
33.
Zhou S, Li H, Zhu Z (2008) Chaos control and synchronization in a fractional neuron network system. Chaos Soliton Fract 36(4):973–984MathSciNetCrossRefMATH
34.
Çelik V, Demir Y (2010) Chaotic fractional order delayed cellular neural network. In: New trends in nanotechnology and fractional calculus applications, pp 313–320
35.
Huang X, Zhao Z, Wang Z, Li Y (2012) Chaos and hyperchaos in fractional-order cellular neural networks. Neurocomput 94:13–21CrossRef
36.
Bhalekar S, Varsha D (2011) A predictor-corrector scheme for solving nonlinear delay differential equations of fractional order. J Fract Calc Appl 1(5):1–9
37.
Qin YX, Liu YQ, Wang L, Zheng ZX (1989) Stability of dynamic systems with delays (in Chinese), 2nd edn. Science Press, BeijingMATH
38.
Hu HY, Wang ZH (2002) Dynamical of control mechanical systems with delayed feed-back. Spring-Verlag, New YorkCrossRef
39.
Guo S (2005) Spatio-temporal patterns of nonlinear oscillations in an excitatory ring network with delay. Nonlinearity 18(5):2391–2407MathSciNetCrossRefMATH
40.
41.
Bungay SD, Campbell SA (2007) Patterns of oscillation in a ring of identical cells with delayed coupling. Int J Bifurc Chaos 17(9):3109–3125MathSciNetCrossRef
42.
Kaslik E, Balint S (2009) Complex and chaotic dynamics in a discretetime-delayed hopfield neural network with ring architecture. Neural Netw 22:1411–1418CrossRef
43.
Liao X, Wong K, Wu Z (2001) Bifurcation analysis on a two-neuron system with distributed delays. Phys D 149:123–141MathSciNetCrossRef
Metadata
Title
Stability Analysis of Fractional-Order Neural Networks with Time Delay
Authors
Hu Wang
Yongguang Yu
Guoguang Wen
Shuo Zhang
Publication date
01-10-2015
Publisher
Springer US
Published in
Neural Processing Letters / Issue 2/2015
Print ISSN: 1370-4621
Electronic ISSN: 1573-773X
DOI
https://doi.org/10.1007/s11063-014-9368-3

Other articles of this Issue 2/2015

Neural Processing Letters 2/2015 Go to the issue

OriginalPaper

Orthogonal Multiset Canonical Correlation Analysis based on Fractional-Order and Its Application in Multiple Feature Extraction and Recognition

OriginalPaper

An Effective Neural Learning Algorithm for Extracting Cross-Correlation Feature Between Two High-Dimensional Data Streams

OriginalPaper

Adaptive Agents in Changing Environments, the Role of Modularity

OriginalPaper

New Criteria on Delay-Dependent Robust Stability for Uncertain Markovian Stochastic Delayed Neural Networks

OriginalPaper

Online Training for Open Faulty RBF Networks

OriginalPaper

Synchronization Analysis of Coupled Stochastic Neural Networks with On–Off Coupling and Time-Delay