Skip to main content
Erschienen in: Neural Processing Letters 2/2014

01.04.2014

New Results on Exponential Convergence for HRNNs with Continuously Distributed Delays in the Leakage Terms

verfasst von: Yuehua Yu, Weidong Jiao

Erschienen in: Neural Processing Letters | Ausgabe 2/2014

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

This paper concerns with exponential convergence for a class of high-order recurrent neural networks with continuously distributed delays in the leakage terms. Without assuming the boundedness on the activation functions, some sufficient conditions are derived to ensure that all solutions of the networks converge exponentially to the zero point by using Lyapunov functional method and differential inequality techniques, which correct some recent results of Chen and Yang (Neural Comput Appl. doi:10.​1007/​s00521-012-1172-2, 2012). Moreover, we propose a new approach to prove the exponential convergence of HRNNs with continuously distributed leakage delays.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

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!

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!

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!

Literatur
1.
Zurück zum Zitat Balasubramaniam P, Vembarasan V, Rakkiyappan R (2012) Global robust asymptotic stability analysis of uncertain switched Hopfield neural networks with time delay in the leakage term. Neural Comput Appl 21(7):1593–1616CrossRef Balasubramaniam P, Vembarasan V, Rakkiyappan R (2012) Global robust asymptotic stability analysis of uncertain switched Hopfield neural networks with time delay in the leakage term. Neural Comput Appl 21(7):1593–1616CrossRef
2.
Zurück zum Zitat Long S, Song Q, Wang X, Li D (2012) Stability analysis of fuzzy cellular neural networks with time delay in the leakage term and impulsive perturbations. J Frankl Inst 349(7):2461–2479CrossRefMathSciNet Long S, Song Q, Wang X, Li D (2012) Stability analysis of fuzzy cellular neural networks with time delay in the leakage term and impulsive perturbations. J Frankl Inst 349(7):2461–2479CrossRefMathSciNet
3.
Zurück zum Zitat Li X, Cao J (2010) Delay-dependent stability of neural networks of neutral type with time delay in the leakage term. Nonlinearity 23(7):1709–1726CrossRefMATHMathSciNet Li X, Cao J (2010) Delay-dependent stability of neural networks of neutral type with time delay in the leakage term. Nonlinearity 23(7):1709–1726CrossRefMATHMathSciNet
4.
Zurück zum Zitat Lakshmanan S, Park JH, Jung HY, Balasubramaniam P (2012) Design of state estimator for neural networks with leakage, discrete and distributed delays. Appl Math Comput 218(22):11297–11310CrossRefMATHMathSciNet Lakshmanan S, Park JH, Jung HY, Balasubramaniam P (2012) Design of state estimator for neural networks with leakage, discrete and distributed delays. Appl Math Comput 218(22):11297–11310CrossRefMATHMathSciNet
6.
Zurück zum Zitat Park MJ, Kwon OM, Park JuH, Lee SM, Cha EJ (2012) Synchronization criteria for coupled neural networks with interval time-varying delays and leakage delay. Appl Math Comput 218(12):6762–6775CrossRefMATHMathSciNet Park MJ, Kwon OM, Park JuH, Lee SM, Cha EJ (2012) Synchronization criteria for coupled neural networks with interval time-varying delays and leakage delay. Appl Math Comput 218(12):6762–6775CrossRefMATHMathSciNet
7.
Zurück zum Zitat Balasubramaniam P, Vembarasan V, Rakkiyappan R (2011) Leakage delays in TS fuzzy cellular neural networks. Neural Process Lett 33(2):111–136CrossRef Balasubramaniam P, Vembarasan V, Rakkiyappan R (2011) Leakage delays in TS fuzzy cellular neural networks. Neural Process Lett 33(2):111–136CrossRef
8.
Zurück zum Zitat Chen Z, Meng J (2012) Exponential convergence for cellular neural networks with time-varying delays in the leakage terms. Abstr Appl Anal. doi:10.1155/2012/941063 Chen Z, Meng J (2012) Exponential convergence for cellular neural networks with time-varying delays in the leakage terms. Abstr Appl Anal. doi:10.​1155/​2012/​941063
9.
Zurück zum Zitat Dembo A, Farotimi O, Kailath T (1991) High-order absolutely stable neural networks. IEEE Trans Circuits Syst 38:57–65CrossRefMATH Dembo A, Farotimi O, Kailath T (1991) High-order absolutely stable neural networks. IEEE Trans Circuits Syst 38:57–65CrossRefMATH
10.
Zurück zum Zitat Psaltis D, Park CH, Hong J (1988) Higher order associative memories and their optical implementations. Neural Netw 1:143–163CrossRef Psaltis D, Park CH, Hong J (1988) Higher order associative memories and their optical implementations. Neural Netw 1:143–163CrossRef
11.
Zurück zum Zitat Karayiannis NB, Venetsanopoulos AN (1995) On the training and performance of high-order neural networks. Math Biosci 129(2):143–168CrossRefMATH Karayiannis NB, Venetsanopoulos AN (1995) On the training and performance of high-order neural networks. Math Biosci 129(2):143–168CrossRefMATH
12.
Zurück zum Zitat Yi X, Shao J, Yu Y, Xiao B (2008) New convergence behavior of high-order Hopfield neural networks with time-varying coefficients. J Comput Appl Math 219:216–222CrossRefMATHMathSciNet Yi X, Shao J, Yu Y, Xiao B (2008) New convergence behavior of high-order Hopfield neural networks with time-varying coefficients. J Comput Appl Math 219:216–222CrossRefMATHMathSciNet
13.
Zurück zum Zitat Shao J (2009) Global exponential convergence for delayed cellular neural networks with a class of general activation functions. Nonlinear Anal Real World Appl 10:1816–1821CrossRefMATHMathSciNet Shao J (2009) Global exponential convergence for delayed cellular neural networks with a class of general activation functions. Nonlinear Anal Real World Appl 10:1816–1821CrossRefMATHMathSciNet
14.
Zurück zum Zitat Huang Z, Peng L, Xu X (2010) Anti-periodic solutions for high-order cellular neural networks with time-varying delays. Electron J Differ Equ 59:1–9 Huang Z, Peng L, Xu X (2010) Anti-periodic solutions for high-order cellular neural networks with time-varying delays. Electron J Differ Equ 59:1–9
15.
Zurück zum Zitat Zhang H, Wang W, Xiao B (2011) Exponential convergence for high-order recurrent neural networks with a class of general activation functions. Appl Math Model 35:123–129CrossRefMATHMathSciNet Zhang H, Wang W, Xiao B (2011) Exponential convergence for high-order recurrent neural networks with a class of general activation functions. Appl Math Model 35:123–129CrossRefMATHMathSciNet
16.
Zurück zum Zitat Wang Y, Lu C, Ji G, Wang L (2011) Global exponential stability of high-order Hopfield-type neural networks with S-type distributed time delays. Commun Nonlinear Sci Numer Simul 16(8):3319–3325CrossRefMATHMathSciNet Wang Y, Lu C, Ji G, Wang L (2011) Global exponential stability of high-order Hopfield-type neural networks with S-type distributed time delays. Commun Nonlinear Sci Numer Simul 16(8):3319–3325CrossRefMATHMathSciNet
17.
Zurück zum Zitat Nie X, Huang Z (2012) Multistability and multiperiodicity of high-order competitive neural networks with a general class of activation functions. Neurocomputing 82(1):1–13CrossRef Nie X, Huang Z (2012) Multistability and multiperiodicity of high-order competitive neural networks with a general class of activation functions. Neurocomputing 82(1):1–13CrossRef
18.
Zurück zum Zitat Liu Q, Xu R (2011) Periodic solutions of high-order Cohen–Grossberg neural networks with distributed delays. Commun Nonlinear Sci Numer Simul 16(7):2887–2893CrossRefMATHMathSciNet Liu Q, Xu R (2011) Periodic solutions of high-order Cohen–Grossberg neural networks with distributed delays. Commun Nonlinear Sci Numer Simul 16(7):2887–2893CrossRefMATHMathSciNet
19.
20.
21.
Zurück zum Zitat Zhang H, Yang M (2013) Global exponential stability of almost periodic solutions for SICNNs with continuously distributed leakage delays. Abstr Appl Anal. doi:10.1155/2013/307981 Zhang H, Yang M (2013) Global exponential stability of almost periodic solutions for SICNNs with continuously distributed leakage delays. Abstr Appl Anal. doi:10.​1155/​2013/​307981
Metadaten
Titel
New Results on Exponential Convergence for HRNNs with Continuously Distributed Delays in the Leakage Terms
verfasst von
Yuehua Yu
Weidong Jiao
Publikationsdatum
01.04.2014
Verlag
Springer US
Erschienen in
Neural Processing Letters / Ausgabe 2/2014
Print ISSN: 1370-4621
Elektronische ISSN: 1573-773X
DOI
https://doi.org/10.1007/s11063-013-9296-7

Weitere Artikel der Ausgabe 2/2014

Neural Processing Letters 2/2014 Zur Ausgabe

Neuer Inhalt