Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Bücher
Zeitschriften
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
ATZ-Fachkongress

Chassis.tech plus 2024


4 Kongresse in einer Veranstaltung

Treffen Sie in München die Fachleute von Chassis, Lenkung, Bremsen sowie Reifen/Räder.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
Introduction Kapitel lesen Erstes Kapitel lesen

2014 | OriginalPaper | Buchkapitel

5. Equilibria of Neural Networks with Impact Activations and Piecewise Constant Argument

verfasst von : Marat Akhmet, Enes Yılmaz

Erschienen in: Neural Networks with Discontinuous/Impact Activations

Verlag: Springer New York

Einloggen

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

search-config
loading …

Abstract

In this chapter we introduce two different types of impulsive neural networks with piecewise constant argument of generalized type called (θ, θ)−type neural networks and (θ, τ)−type neural networks, respectively. For these types, sufficient conditions for existence of a unique equilibrium are obtained, existence and uniqueness of solutions and an equivalence lemma for such systems are established, and stability criterion for the equilibrium based on linear approximation is proposed.

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!

Jetzt informieren

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!

Jetzt informieren

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!

Jetzt informieren
Vorheriges Kapitel Periodic Motions and Equilibria of Neural Networks with Piecewise Constant Argument
Nächstes Kapitel Periodic Motions of Neural Networks with Impact Activations and Piecewise Constant Argument
Literatur
10.
Akça H, Alassar R, Covachev V, Covacheva Z, Al-Zahrani E (2004) Continuous-time additive Hopfield-type neural networks with impulses. J Math Anal Appl 290:436–451MathSciNetCrossRefMATH
13.
Akhmet MU (2006) On the integral manifolds of the differential equations with piecewise constant argument of generalized type. In: Agarval RP, Perera K (eds) Proceedings of the conference on differential and difference equations at the florida institute of technology, Melbourne, Florida, 1–5 August 2005. Hindawi Publishing Corporation, Nasr City, pp 11–20
14.
Akhmet MU (2007) Integral manifolds of differential equations with piecewise constant argument of generalized type. Nonlin Anal 66:367–383MathSciNetCrossRefMATH
15.
Akhmet MU (2007) On the reduction principle for differential equations with piecewise constant argument of generalized type. J Math Anal Appl 336:646–663MathSciNetCrossRefMATH
18.
Akhmet MU (2008) Stability of differential equations with piecewise constant arguments of generalized type. Nonlinear Anal 68:794–803MathSciNetCrossRefMATH
23.
24.
Akhmet M (2011) Nonlinear hybrid continuous/discrete time models. Atlantis, Amsterdam-ParisCrossRef
29.
Akhmet MU, Aruğaslan D (2009) Lyapunov-Razumikhin method for differential equations with piecewise constant argument. Discrete Contin Dyn Syst 25(2):457–466MathSciNetCrossRefMATH
39.
Akhmet MU, Yılmaz E (2010) Impulsive Hopfield-type neural network system with piecewise constant argument. Nonlin Anal Real World Appl 11:2584–2593CrossRefMATH
45.
Akhmet MU, Aruğaslan D, Yılmaz E (2010) Stability analysis of recurrent neural networks with piecewise constant argument of generalized type. Neural Network 23:305–311CrossRef
68.
72.
Cao JD, Zhou DM (1998) Stability analysis of delayed cellular neural networks. Neural Networks 11: 1601–1605CrossRef
78.
Chua LO, Roska T (1992) Cellular neural networks with nonlinear and delay type template elements and non-uniform grids. Int J Circuit Theory Appl 20:449–451CrossRef
79.
80.
83.
Civalleri PP, Gilli M, Pandolfi L (1993) On stability of cellular neural networks with delay. IEEE Trans Circuits Syst I 40:157–164MathSciNetCrossRefMATH
84.
Cohen MA, Grossberg S (1983) Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Transact SMC-13 pp 815–826MathSciNet
88.
93.
Coombes S, Bressloff PC (2000) Solitary waves in a model of dendritic cable with active spines. SIAM J Appl Math 61(2):432–453MathSciNetCrossRefMATH
100.
Driessche PVD, Zou X (1998) Global attractivity in delayed Hopfield neural network models. SIAM J Appl Math 58(6):1878–1890MathSciNetCrossRefMATH
102.
108.
Gopalsamy K (1992) Stability and oscillation in delay differential equations of population dynamics. Kluwer Academic Publishers, DordrechtCrossRef
109.
117.
Guan ZH, Chen G (1999) On delayed impulsive Hopfield neural networks. Neural Netw 12:273–280CrossRef
118.
Guan ZH, Lam J, Chen G (2000) On impulsive autoassociative neural networks. Neural Netw 13:63–69CrossRef
141.
Hopfield JJ (1984) Neurons with graded response have collective computational properties like those of two-stage neurons. Proc Nat Acad Sci Biol 81:3088–3092CrossRef
148.
Huang H, Cao J, Wang J (2002) Global exponential stability and periodic solutions of recurrent neural networks with delays. Phys Lett A 298:393–404MathSciNetCrossRefMATH
149.
Huang H, Hob DWC, Cao J (2005) Analysis of global exponential stability and periodic solutions of neural networks with time-varying delays. Neural Netw 18:161–170CrossRef
153.
Huang Z, Wang X, Xia Y (2009) A topological approach to the existence of solutions for nonlinear differential equations with piecewise constant argument. Chaos Soliton Fract 39(3):1121–1131MathSciNetCrossRefMATH
156.
Keener JP, Hoppensteadt FC, Rinzel J (1981) Integrate-and-fire models of nerve membrane response to oscillatory input. SIAM J Appl Math 41(3):503–517MathSciNetCrossRef
160.
171.
Lakshmikantham V, Bainov DD, Simeonov PS (1989) Theory of impulsive differential equations. Modern applied mathematics, World Scientific, SingaporeCrossRefMATH
175.
Li XM, Huang L, Zhu H (2003) Global stability of cellular neural networks with constant and variable delays. Nonlinear Anal 53:319–333MathSciNetCrossRefMATH
189.
192.
193.
Mohammad S (2007) Exponential stability in Hopfield-type neural networks with impulses. Chaos Solitons Fract 32:456–467CrossRef
217.
Pavlidis T (1965) A new model for simple neural nets and its application in the design of a neural oscillator. B Math Biol 27(2):215–229MathSciNetMATH
231.
Samoilenko AM, Perestyuk NA (1995) Impulsive differential equations. World Scientific, SingaporeMATH
242.
243.
Townley S, Ilchmann A, Weib MG, Mcclements W, Ruiz AC, Owens DH, Pratzel-Wolters D (2000) Existence and learning of oscillations in recurrent neural networks. IEEE Trans Neural Networks 11(1):205–214CrossRef
261.
Wiener J (1993) Generalized solutions of functional differential equations. World Scientific, SingaporeMATH
275.
279.
Xu S, Chu Y, Lu J (2006) New results on global exponential stability of recurrent neural networks with time-varying delays. Phys Lett A 352:371–379CrossRefMATH
286.
Yang Y, Cao J (2007) Stability and periodicity in delayed cellular neural networks with impulsive effects. Nonlinear Anal:Real World Appl 8:362–374MathSciNetCrossRefMATH
292.
Yucel E, Arik S (2004) New exponential stability results for delayed neural networks with time varying delays. Physica D 191:14–322MathSciNetCrossRef
294.
Zeng Z, Wang J (2006) Improved conditions for global exponential stability of recurrent neural networks with time-varying delays. IEEE Transact On Neural Netw 17(3):623–635MathSciNetCrossRef
298.
Zhang Y, Sun J (2005) Stability of impulsive neural networks with time delays. Phys Lett A 348:44–50CrossRefMATH
Metadaten
Titel
Equilibria of Neural Networks with Impact Activations and Piecewise Constant Argument
verfasst von
Marat Akhmet
Enes Yılmaz
Copyright-Jahr
2014
Verlag
Springer New York
Buch
Neural Networks with Discontinuous/Impact Activations

Print ISBN: 978-1-4614-8565-0

Electronic ISBN: 978-1-4614-8566-7

Copyright-Jahr: 2014

DOI
https://doi.org/10.1007/978-1-4614-8566-7_5

Premium Partner

    Bildnachweise