Skip to main content
Erschienen in: International Journal of Machine Learning and Cybernetics 4/2017

11.02.2016 | Original Article

Almost periodic solutions for fuzzy cellular neural networks with multi-proportional delays

verfasst von: Zuda Huang

Erschienen in: International Journal of Machine Learning and Cybernetics | Ausgabe 4/2017

Einloggen

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

search-config
loading …

Abstract

In this paper, a class of fuzzy cellular neural networks with multi-proportional delays is investigated. By applying contraction mapping fixed point theorem and differential inequality techniques, some sufficient conditions are established for the existence and global attractivity of a unique almost periodic solution for the model, which improve and supplement existing ones. Moreover, a numerical example is given to illustrate the feasibility and application of the obtained results.

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!

Weitere Produktempfehlungen anzeigen
Literatur
2.
Zurück zum Zitat Bao H (2015) Existence and exponential stability of periodic solution for BAM Fuzzy CohenCGrossberg neural networks with mixed delays. Neural Process Lett. doi:10.1007/s11063-015-9455-0 Bao H (2015) Existence and exponential stability of periodic solution for BAM Fuzzy CohenCGrossberg neural networks with mixed delays. Neural Process Lett. doi:10.​1007/​s11063-015-9455-0
3.
Zurück zum Zitat Derfel GA (1982) On the behaviour of the solutions of functional and functional-differential equations with several deviating arguments. Ukr Math J 34:286–291CrossRefMATH Derfel GA (1982) On the behaviour of the solutions of functional and functional-differential equations with several deviating arguments. Ukr Math J 34:286–291CrossRefMATH
4.
Zurück zum Zitat Derfel GA (1990) Kato problem for functional-differential equations and difference Schr\(\ddot{o}\)dinger operators. Oper Theor 46:319–321MATH Derfel GA (1990) Kato problem for functional-differential equations and difference Schr\(\ddot{o}\)dinger operators. Oper Theor 46:319–321MATH
5.
Zurück zum Zitat Dovrolis C, Stiliadisd D, Ramanathan P (1999) Proportional differentiated services: delay differentiation and packet scheduling. ACM Sigcomm Comput Commun Rev 29(4):109–120CrossRef Dovrolis C, Stiliadisd D, Ramanathan P (1999) Proportional differentiated services: delay differentiation and packet scheduling. ACM Sigcomm Comput Commun Rev 29(4):109–120CrossRef
6.
Zurück zum Zitat Fink AM (1974) Almost periodic differential equations, vol 377. Lecture Notes in MathematicsSpringer, Berlin Fink AM (1974) Almost periodic differential equations, vol 377. Lecture Notes in MathematicsSpringer, Berlin
7.
8.
Zurück zum Zitat Hale JK, Verduyn Lunel SM (1993) Introduction to functional differential equations. New York: Springer-Verlag Hale JK, Verduyn Lunel SM (1993) Introduction to functional differential equations. New York: Springer-Verlag
9.
Zurück zum Zitat Jian J, Jiang W (2015) Lagrange exponential stability for fuzzy Cohen-Grossberg neural networks with time-varying delays. Fuzzy Sets Syst 277:65–80MathSciNetCrossRef Jian J, Jiang W (2015) Lagrange exponential stability for fuzzy Cohen-Grossberg neural networks with time-varying delays. Fuzzy Sets Syst 277:65–80MathSciNetCrossRef
10.
Zurück zum Zitat Liu B, Tunc C (2015) Pseudo almost periodic solutions for CNNs with leakage delays and complex deviating arguments. Neural Comput Appl 26:429–435CrossRef Liu B, Tunc C (2015) Pseudo almost periodic solutions for CNNs with leakage delays and complex deviating arguments. Neural Comput Appl 26:429–435CrossRef
11.
Zurück zum Zitat Liu B (2015) Pseudo almost periodic solutions for neutral type CNNs with continuously distributed leakage delays. Neurocomputing 148:445–454CrossRef Liu B (2015) Pseudo almost periodic solutions for neutral type CNNs with continuously distributed leakage delays. Neurocomputing 148:445–454CrossRef
12.
Zurück zum Zitat Liu B (2015) Pseudo almost periodic solutions for CNNs with continuously distributed leakage delays. Neural Process Lett 42:233–256CrossRef Liu B (2015) Pseudo almost periodic solutions for CNNs with continuously distributed leakage delays. Neural Process Lett 42:233–256CrossRef
13.
Zurück zum Zitat Liu B, Huang L (2005) Existence and exponential stability of almost periodic solutions for cellular neural networks with time-varying delays. Phys Lett A 341(1–4):135–144CrossRefMATH Liu B, Huang L (2005) Existence and exponential stability of almost periodic solutions for cellular neural networks with time-varying delays. Phys Lett A 341(1–4):135–144CrossRefMATH
14.
Zurück zum Zitat Liu B, Huang L (2008) Positive almost periodic solutions for recurrent neural networks. Nonlinear Anal Real World Appl 9:830–841MathSciNetCrossRefMATH Liu B, Huang L (2008) Positive almost periodic solutions for recurrent neural networks. Nonlinear Anal Real World Appl 9:830–841MathSciNetCrossRefMATH
15.
Zurück zum Zitat Lu W, Chen T (2005) Global exponential stability of almost periodic solutions for a large class of delayed dynamical systems. Sci China Ser A Math 8(48):1015–1026MathSciNetCrossRefMATH Lu W, Chen T (2005) Global exponential stability of almost periodic solutions for a large class of delayed dynamical systems. Sci China Ser A Math 8(48):1015–1026MathSciNetCrossRefMATH
16.
Zurück zum Zitat Niu S, Jiang H, Zhidong Teng (2008) Exponential stability and periodic solutions of FCNNs with variable coefficients and time-varying delays. Neurocomputing 71:2929–2936CrossRef Niu S, Jiang H, Zhidong Teng (2008) Exponential stability and periodic solutions of FCNNs with variable coefficients and time-varying delays. Neurocomputing 71:2929–2936CrossRef
17.
Zurück zum Zitat Niu S, Jiang H, Zhidong Teng (2009) Periodic oscillation of FCNNs with distributed delays and variable coefficients. Nonlinear Anal Real World Appl 10:1540–1554MathSciNetCrossRefMATH Niu S, Jiang H, Zhidong Teng (2009) Periodic oscillation of FCNNs with distributed delays and variable coefficients. Nonlinear Anal Real World Appl 10:1540–1554MathSciNetCrossRefMATH
18.
Zurück zum Zitat Ockendon JR, Tayler AB (1971) The dynamics of a current collection systemfor an electric locomotive. Proc R Soc A 322:447–468CrossRef Ockendon JR, Tayler AB (1971) The dynamics of a current collection systemfor an electric locomotive. Proc R Soc A 322:447–468CrossRef
19.
Zurück zum Zitat Song Q, Wang Z (2009) Dynamical behaviors of fuzzy reaction-diffusion periodic cellular neural networks with variable coefficients and delays. Appl Math Model 33:3533–3545MathSciNetCrossRefMATH Song Q, Wang Z (2009) Dynamical behaviors of fuzzy reaction-diffusion periodic cellular neural networks with variable coefficients and delays. Appl Math Model 33:3533–3545MathSciNetCrossRefMATH
20.
Zurück zum Zitat Song X, Zhao P, Xing Z, Peng J (2015) Global asymptotic stability of CNNs with impulses and multi-proportional delays. Math Meth Appl Sci. doi:10.1002/mma.3515 Song X, Zhao P, Xing Z, Peng J (2015) Global asymptotic stability of CNNs with impulses and multi-proportional delays. Math Meth Appl Sci. doi:10.​1002/​mma.​3515
21.
Zurück zum Zitat Wu J (2001) Introduction to neural dynamics and signal trasmission delay. Walter de Gruyter, BelinCrossRef Wu J (2001) Introduction to neural dynamics and signal trasmission delay. Walter de Gruyter, BelinCrossRef
22.
Zurück zum Zitat Xu Y (2014) New results on almost periodic solutions for CNNs with time-varying leakage delays. Neural Comput Appl 25:1293–1302CrossRef Xu Y (2014) New results on almost periodic solutions for CNNs with time-varying leakage delays. Neural Comput Appl 25:1293–1302CrossRef
23.
Zurück zum Zitat Yang HZ, Sheng L (2009) Robust stability of uncertain stochastic fuzzy cellular neural networks. Neurocomputing 73:133–138CrossRef Yang HZ, Sheng L (2009) Robust stability of uncertain stochastic fuzzy cellular neural networks. Neurocomputing 73:133–138CrossRef
24.
Zurück zum Zitat Yang T, Yang L, Wu C, Chua L (1996) Fuzzy cellular neural networks:theory. In: Proceedings of IEEE International Work shop on Cellular Neural Networks and Applications, pp 181–186 Yang T, Yang L, Wu C, Chua L (1996) Fuzzy cellular neural networks:theory. In: Proceedings of IEEE International Work shop on Cellular Neural Networks and Applications, pp 181–186
25.
Zurück zum Zitat Yang W (2014) Periodic solution for Fuzzy Cohen-Grossberg BAM neural networks with both time-varying and distributed delays and variable coefficients. Neural Process Lett 40:51–73CrossRef Yang W (2014) Periodic solution for Fuzzy Cohen-Grossberg BAM neural networks with both time-varying and distributed delays and variable coefficients. Neural Process Lett 40:51–73CrossRef
26.
Zurück zum Zitat Yuan K, Cao JD, Deng JM (2006) Exponential stability and periodic solutions of fuzzy cellular neural networks with time-varying delays. Neurocomputing 69(13–15):1619–1627CrossRef Yuan K, Cao JD, Deng JM (2006) Exponential stability and periodic solutions of fuzzy cellular neural networks with time-varying delays. Neurocomputing 69(13–15):1619–1627CrossRef
27.
Zurück zum Zitat Zhang H (2014) Existence and stability of almost periodic solutions for CNNs with continuously distributed leakage delays. Neural Comput Appli 2014(24):1135–1146CrossRef Zhang H (2014) Existence and stability of almost periodic solutions for CNNs with continuously distributed leakage delays. Neural Comput Appli 2014(24):1135–1146CrossRef
28.
Zurück zum Zitat Zhang H, Shao J (2013) Existence and exponential stability of almost periodic solutions for CNNs with time-varying leakage delays. Neurocomputing 121(9):226–233CrossRef Zhang H, Shao J (2013) Existence and exponential stability of almost periodic solutions for CNNs with time-varying leakage delays. Neurocomputing 121(9):226–233CrossRef
29.
Zurück zum Zitat Zhang H, Shao J (2013) Almost periodic solutions for cellular neural networks with time-varying delays in leakage terms. Appl Math Comput 219(24):11471–11482MathSciNetMATH Zhang H, Shao J (2013) Almost periodic solutions for cellular neural networks with time-varying delays in leakage terms. Appl Math Comput 219(24):11471–11482MathSciNetMATH
30.
Zurück zum Zitat Zhang Y, Zhou L (2012) Exponential stability of a class of cellular neural networks with multi-pantograph delays. Acta Electron Sin 40(6):1159–1163 Zhang Y, Zhou L (2012) Exponential stability of a class of cellular neural networks with multi-pantograph delays. Acta Electron Sin 40(6):1159–1163
31.
Zurück zum Zitat Zheng CD, Zhang X, Wang Z (2015) Mode-dependent stochastic stability criteria of fuzzy Markovian jumping neural networks with mixed delays. ISA Trans 56:8–17CrossRef Zheng CD, Zhang X, Wang Z (2015) Mode-dependent stochastic stability criteria of fuzzy Markovian jumping neural networks with mixed delays. ISA Trans 56:8–17CrossRef
32.
Zurück zum Zitat Zhou L (2013) Delay-dependent exponential stability of Cellular neural networks with multi-proportional delays. Neural Process Lett 38:347–359CrossRef Zhou L (2013) Delay-dependent exponential stability of Cellular neural networks with multi-proportional delays. Neural Process Lett 38:347–359CrossRef
33.
Zurück zum Zitat Zhou L (2015) Novel global exponential stability criteria for hybrid BAM neural networks with proportional delays. Neurocomputing 161 Zhou L (2015) Novel global exponential stability criteria for hybrid BAM neural networks with proportional delays. Neurocomputing 161
34.
Zurück zum Zitat Zhou L, Zhang Y (2015) Global exponential stability of cellular neural networks with multi-proportional delays. Int J Biomath 8(6):1550071, 1–17 Zhou L, Zhang Y (2015) Global exponential stability of cellular neural networks with multi-proportional delays. Int J Biomath 8(6):1550071, 1–17
35.
Zurück zum Zitat Zhou L, Liu J (2013) Global asymptotic stability of a class of cellular neural networks with proportional delays. Chin J Eng Math 5(30):673–682, 99–106 Zhou L, Liu J (2013) Global asymptotic stability of a class of cellular neural networks with proportional delays. Chin J Eng Math 5(30):673–682, 99–106
Metadaten
Titel
Almost periodic solutions for fuzzy cellular neural networks with multi-proportional delays
verfasst von
Zuda Huang
Publikationsdatum
11.02.2016
Verlag
Springer Berlin Heidelberg
Erschienen in
International Journal of Machine Learning and Cybernetics / Ausgabe 4/2017
Print ISSN: 1868-8071
Elektronische ISSN: 1868-808X
DOI
https://doi.org/10.1007/s13042-016-0507-1

Weitere Artikel der Ausgabe 4/2017

International Journal of Machine Learning and Cybernetics 4/2017 Zur Ausgabe

Neuer Inhalt