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Dynamics and Oscillations of GHNNs with Time-Varying Delay

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Artificial Neural Networks and Machine Learning – ICANN 2012 (ICANN 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7552))

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Abstract

In this paper, we investigate the dynamics and the global exponential stability of the Hopfield Neural network with time-varying delay and variable coefficients. For this purpose, the activation functions are assumed to be globally Lipschitz continuous. The properties of norms and the contraction principle are adjusted to ensure the existence as well as the uniqueness of the the pseudo almost automorphic solution. Then by employing suitable analytic techniques, global attractivity of the unique pseudo almost automorphic solution is established.

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References

  1. Ammar, B., Chérif, F., Alimi, M.A.: Existence and Uniqueness of Pseudo Almost-Periodic Solutions of Recurrent Neural Networks with Time-Varying Coefficients and Mixed Delays. IEEE Transactions on Neural Networks and Learning Systems 23(1), 109–118 (2012)

    Article  Google Scholar 

  2. Bai, C.: Existence and stability of almost periodic solutions of HNNs with continuously distributed delays. Nonlinear Analysis 71, 5850–5859 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  3. Cieutat, P., Fatajou, S., N’Guéré kata, G.M.: Composition of pseudo almost periodic and pseudo almost automorphic functions and applications to evolution equations. Applicable Analysis 89(1), 11–27 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  4. Ding, H.S., Liang, J., N’Guérékata, G.M., Xiao, T.J.: Pseudo almost periodicity of some nonautonomous evolution equations with delay. Nonlinear Anal. TMA 67, 1412–1418 (2007)

    Article  MATH  Google Scholar 

  5. Dong, Q., Matsui, K., Haung, X.: Existence and stability of periodic solutions for Hopfield neural network equations with periodic input. Nonlinear Anal. 49, 471–479 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  6. Zhao, H.: Existence and global attractivity of almost periodic solution for cellular neural network with distributed delays. Applied Math. Computation 154, 683–695 (2004)

    Article  MATH  Google Scholar 

  7. Gui, Z., Ge, W., Yang, X.: Periodic oscillation for a Hopfield neural networks with neutral delays. Phys. Lett. A. 364, 267–273 (2007)

    Article  MATH  Google Scholar 

  8. Hopfield, J.: Neurons with graded response have collective computational properties like those of two-state neurons. Proc. Nat. Acad. Sci. USA. 81, 3088–3092 (1984)

    Article  Google Scholar 

  9. Liang, J., Zhang, J., Xiao, T.J., Liang, J., Zhang, J.J., Xiao, T.-J.: Composition of pseudo almost automorphic and asymptotically almost automorphic functions, J. Math. Anal. Appl. 340, 1493–1499 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  10. Li, Y., Zhang, T.: Existence of almost periodic solutions for Hopfield neural networks with continuously distributed delays and impulses. EJDE 152, 1–8 (2009)

    Google Scholar 

  11. Liu, B., Huang, L.: Existence and global exponential stability of almost periodic solutions for Hopfield neural networks with delays. Neurocomputing 68, 196–207 (2005)

    Article  Google Scholar 

  12. Liu, Z., Chen, A., Cao, J., Huang, L.: Existence and global exponential stability of almost periodic solutions of BAM neural networks with continuously distributed delays. Phys. Lett. A 319, 305–316 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  13. Liu, B.: Almost periodic solutions for Hopfield neural networks with continuously distributed delays. Math. Comput. Simulation. 73, 327–335 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  14. Liu, Y., You, Z., Cao, L.: On the almost periodic solutions of GHNNs with time-varying delays. Neurocomputing 69, 1760–1767 (2006)

    Article  Google Scholar 

  15. Xiao, T.J., Liang, J., Zhang, J.: Pseudo almost automorphic solutions to semilinear differential equations in Banach space. Semigroup Forum 76, 518–524 (2008)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. ISSATS, Laboratory of Math Physics, Specials Functions and Applications LR11ES35, Ecole Supérieure des Sciences et de Technologie, 4002, Sousse, Tunisia

    Farouk Chérif

Authors
  1. Farouk Chérif
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Editor information

Editors and Affiliations

  1. Neuro Heuristic Research Group, University of Lausanne, 1015, Lausanne, Switzerland

    Alessandro E. P. Villa

  2. Department of Informatics, Nicolaus Copernicus University, 87-100, Toruń, Poland

    Włodzisław Duch

  3. Center for Complex Systems Studies, Kalamazoo College, 49006, Kalamazoo, MI, USA

    Péter Érdi

  4. Dipartimento di Informatica e Scienze dell’Informazione, Università di Genova, 16146, Genoa, Italy

    Francesco Masulli

  5. Institut für Neuroinformatik, Universität Ulm, 89069, Ulm, Germany

    Günther Palm

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© 2012 Springer-Verlag Berlin Heidelberg

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Chérif, F. (2012). Dynamics and Oscillations of GHNNs with Time-Varying Delay. In: Villa, A.E.P., Duch, W., Érdi, P., Masulli, F., Palm, G. (eds) Artificial Neural Networks and Machine Learning – ICANN 2012. ICANN 2012. Lecture Notes in Computer Science, vol 7552. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33269-2_3

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  • DOI: https://doi.org/10.1007/978-3-642-33269-2_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33268-5

  • Online ISBN: 978-3-642-33269-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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