Skip to main content
Top
Published in: Neural Computing and Applications 1/2013

01-01-2013 | Original Article

Stability of Hopfield neural networks with time delays and variable-time impulses

Authors: Chao Liu, Chuandong Li, Tingwen Huang, Chaojie Li

Published in: Neural Computing and Applications | Issue 1/2013

Log in

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

search-config
loading …

Abstract

The stability of Hopfield neural networks with fixed-time impulses has been intensively investigated in recent years. However, few existing publications addressed the stability of delayed neural networks with variable-time impulses. In this paper, we consider the case of variable-time impulses and attempt to establish the general stability criteria. It shows that the proposed results can also be applied to the case of fixed-time impulses, which provide a new stability condition for the case of fixed-time impulses. To illustrate the effectiveness of our theoretical results, numerical examples and simulations are also presented.

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

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+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!

Literature
1.
go back to reference Akca H, Alassar R, Covachev V, Covacheva Z, Al-Zahrani E (2004) Continuous-time additive Hopfield-type neural network with impulses. J Math Anal Appl 290:436–451MathSciNetMATHCrossRef Akca H, Alassar R, Covachev V, Covacheva Z, Al-Zahrani E (2004) Continuous-time additive Hopfield-type neural network with impulses. J Math Anal Appl 290:436–451MathSciNetMATHCrossRef
2.
go back to reference Berman A, Plemmons RJ (1979) Nonnegative matrices in mathematical sciences. Academic Press, New YorkMATH Berman A, Plemmons RJ (1979) Nonnegative matrices in mathematical sciences. Academic Press, New YorkMATH
3.
go back to reference Chen T (2001) Global exponential stability of delayed Hopfield neural networks. Neural Netw 14:977–980CrossRef Chen T (2001) Global exponential stability of delayed Hopfield neural networks. Neural Netw 14:977–980CrossRef
4.
go back to reference Fu XL, Qi JG, Liu YS (2000) General comparison principle for impulsive variable time differential equations with application. Nonlinear Anal 42:1421–1429MathSciNetMATHCrossRef Fu XL, Qi JG, Liu YS (2000) General comparison principle for impulsive variable time differential equations with application. Nonlinear Anal 42:1421–1429MathSciNetMATHCrossRef
6.
go back to reference Guan ZH, Chen G (1999) On delayed impulsive Hopfield neural networks. Neural Netw 12:273–280CrossRef Guan ZH, Chen G (1999) On delayed impulsive Hopfield neural networks. Neural Netw 12:273–280CrossRef
7.
go back to reference Guan ZH, Chen GR, Qin Y (2000) On equilibria, stability, and instability of Hopfield neural networks. IEEE Trans Neural Netw 11:534–540CrossRef Guan ZH, Chen GR, Qin Y (2000) On equilibria, stability, and instability of Hopfield neural networks. IEEE Trans Neural Netw 11:534–540CrossRef
8.
go back to reference Hopfield JJ (1984) Neurons with graded response have collective computational properties like those of two-state neurons. Proc Natl Acad Sci USA Biophys 81:3088–3092CrossRef Hopfield JJ (1984) Neurons with graded response have collective computational properties like those of two-state neurons. Proc Natl Acad Sci USA Biophys 81:3088–3092CrossRef
9.
go back to reference Huang ZT, Yang QG, Luo XS (2008) Exponential stability of impulsive neural networks with time-varying delays. Chaos Solitons Fractals 35:770–780MATHCrossRef Huang ZT, Yang QG, Luo XS (2008) Exponential stability of impulsive neural networks with time-varying delays. Chaos Solitons Fractals 35:770–780MATHCrossRef
10.
go back to reference Juang JC (1999) Stability analysis of Hopfield-type neural networks. IEEE Trans Neural Netw 10:1366–1374CrossRef Juang JC (1999) Stability analysis of Hopfield-type neural networks. IEEE Trans Neural Netw 10:1366–1374CrossRef
11.
go back to reference Kaul SK (1997) Vector lyapunov functions in impulsive variable-time differential systems. Nonlinear Anal Theory Methods Appl 30:2695–2698MathSciNetMATHCrossRef Kaul SK (1997) Vector lyapunov functions in impulsive variable-time differential systems. Nonlinear Anal Theory Methods Appl 30:2695–2698MathSciNetMATHCrossRef
12.
go back to reference Lakshmikantham V, Bainov DD, Simeonov PS (1989) Theory of impulsive differential equations. World Scientific, SingaporeMATHCrossRef Lakshmikantham V, Bainov DD, Simeonov PS (1989) Theory of impulsive differential equations. World Scientific, SingaporeMATHCrossRef
13.
go back to reference Lakshmikantham V, Leela S, Kaul S (1994) Comparison principle for impulsive differential equations with variable times and stability theory. Nonlinear Anal 22:499–503MathSciNetMATHCrossRef Lakshmikantham V, Leela S, Kaul S (1994) Comparison principle for impulsive differential equations with variable times and stability theory. Nonlinear Anal 22:499–503MathSciNetMATHCrossRef
14.
go back to reference Lee DL (1999) New stability conditions for Hopfield networks in partial simultaneous update mode. IEEE Trans Neural Netw 10:975–978CrossRef Lee DL (1999) New stability conditions for Hopfield networks in partial simultaneous update mode. IEEE Trans Neural Netw 10:975–978CrossRef
15.
go back to reference Li CD, Li CJ, Liu C (2009) Destabilizing effects of impulsive in delayed BAM neural networks. Modern Phys Lett B 23:3503–3513MATHCrossRef Li CD, Li CJ, Liu C (2009) Destabilizing effects of impulsive in delayed BAM neural networks. Modern Phys Lett B 23:3503–3513MATHCrossRef
16.
go back to reference Li CJ, Li CD, Liao XF et al (2011) Impulsive effects on stability of high-order BAM neural networks with time-delays. Neurocomputing 74:1541–1550CrossRef Li CJ, Li CD, Liao XF et al (2011) Impulsive effects on stability of high-order BAM neural networks with time-delays. Neurocomputing 74:1541–1550CrossRef
17.
go back to reference Liang XB (2000) Equivalence between local exponential stability of the unique equilibrium point and global stability for Hopfield-type neural networks with two neurons. IEEE Trans Neural Netw 11:1194–1196CrossRef Liang XB (2000) Equivalence between local exponential stability of the unique equilibrium point and global stability for Hopfield-type neural networks with two neurons. IEEE Trans Neural Netw 11:1194–1196CrossRef
18.
go back to reference Liu X, Ballinger G (2002) Existence and continuability of solutions for differential equations with delays and state-dependent impulses. Nonlinear Anal 51:633–647MathSciNetMATHCrossRef Liu X, Ballinger G (2002) Existence and continuability of solutions for differential equations with delays and state-dependent impulses. Nonlinear Anal 51:633–647MathSciNetMATHCrossRef
20.
go back to reference Long SJ, Xu DY (2008) Delay-dependent stability analysis for impulsive neural networks with time varying delays. Neurocomputing 71:1705–1713CrossRef Long SJ, Xu DY (2008) Delay-dependent stability analysis for impulsive neural networks with time varying delays. Neurocomputing 71:1705–1713CrossRef
21.
22.
23.
24.
go back to reference Yang XF (2005) Existence and stability of periodic solution in impulsive Hopfield neural networks with finite distribute delays. Phys Lett A 343:108–116MATHCrossRef Yang XF (2005) Existence and stability of periodic solution in impulsive Hopfield neural networks with finite distribute delays. Phys Lett A 343:108–116MATHCrossRef
25.
go back to reference Yang H, Dillon TS (1994) Exponential stability and oscillation of Hopfield graded response neural network. IEEE Trans Neural Netw 5:719–729CrossRef Yang H, Dillon TS (1994) Exponential stability and oscillation of Hopfield graded response neural network. IEEE Trans Neural Netw 5:719–729CrossRef
Metadata
Title
Stability of Hopfield neural networks with time delays and variable-time impulses
Authors
Chao Liu
Chuandong Li
Tingwen Huang
Chaojie Li
Publication date
01-01-2013
Publisher
Springer-Verlag
Published in
Neural Computing and Applications / Issue 1/2013
Print ISSN: 0941-0643
Electronic ISSN: 1433-3058
DOI
https://doi.org/10.1007/s00521-011-0695-2

Other articles of this Issue 1/2013

Neural Computing and Applications 1/2013 Go to the issue

Premium Partner