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Existence and Global Attractability of Almost Periodic Solution for Competitive Neural Networks with Time-Varying Delays and Different Time Scales

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Advances in Neural Networks - ISNN 2006 (ISNN 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3971))

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Abstract

The dynamics of cortical cognitive maps developed by self-organization must include the aspects of long and short-term memory. The behavior of such a neural network is characterized by an equation of neural activity as a fast phenomenon and an equation of synaptic modification as a slow part of the neural system, besides,this model bases on unsupervised synaptic learning algorithm. Considered the effect of time delays, we prove the existence, uniqueness and global attraction of the almost periodic solution by using fixed theorem and Variation-of-constants formula.

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References

  1. Meyer-Baese, A., Pilyugin, S.S., Chen, Y.: Global Exponential Stability of Competitive Neural Networks with Different Time Scale. IEEE Trans. Neural Networks 14(5), 716–719 (2003)

    Article  Google Scholar 

  2. Jin, L., Gupta, M.: Stabale Dynamic Backpropagation Learning in Recurrent Neural Networks. IEEE Trans. Neural Networks 10(11), 1321–1334 (1999)

    Google Scholar 

  3. Galicki, M., Leistitz, L., Witte, H.: Learning Continuous Trajectories in Recurrent Neural Networks with Time-dependent Weights. IEEE Trans. Neural Networks 10(5), 741–756 (1999)

    Article  Google Scholar 

  4. Suykens, J., Moor, B., Vandewalle, J.: Robust local Stability of Multilayer Recurrent Neural Networks. IEEE Trans. Neural Networks 11(1), 222–229 (2000)

    Article  Google Scholar 

  5. Wang, L.S., Xu, D.Y.: Stability Analysis of Hopfield Neural Networks with Time Delay. Applied Mathematics and Mechanics 23, 250–252 (2002)

    Google Scholar 

  6. Grossberg, S.: Competition,Decision and Consensus. J. Math. Anal. Applicat. 66, 470–493 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  7. Amari, S.: Competitive and Cooperater Aspects in Dynamics of Neural Excition and Self-organization. Competition Cooperation Neural Networks 20, 1–28 (1982)

    Google Scholar 

  8. He, C.Y.: Almost Periodic Differential Equations. Higher Education Publishing House, Beijing (1992)

    Google Scholar 

  9. Zhao, H.Y., Wang, G.L.: Existence and Global Atrractivity of Almost Periodic Solutions for Hopfield Neural Networks with Variable Delay. Acta Mathematica Scientia A 24(6), 723–726 (2004)

    MATH  Google Scholar 

  10. Lu, W., Chen, T.: Global Exponential Stability of Almost Periodic Trajectory of a Large Class of Delayed Dynamical Systems. Science in China A. Mathematics, 1015–1026 (2005)

    Google Scholar 

  11. Cao, J.D., Chen, A.P., Huang, X.: Almost Periodic Attractor of Delayed Neural Networks with Variable Coefficients. Physics letters A 340, 104–120 (2005)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Ocean University of China, Qingdao, 266071, People’s Republic of China

    Wentong Liao & Linshan Wang

Authors
  1. Wentong Liao
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  2. Linshan Wang
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Editor information

Editors and Affiliations

  1. Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, China

    Jun Wang

  2. Computational Intelligence Laboratory, School of Computer Science and Engineering, University of Electronic Science and Technology of China, 610054, Chengdu, P.R. China

    Zhang Yi

  3. Department of Electrical Engineering, University of Louisville, 40292, Louisville, KY, U.S.A

    Jacek M. Zurada

  4. Laboratory for Computational Biology, Shanghai Center for Systems Biomedicine, 800 Dong Chuan Rd., 200240, Shanghai, China

    Bao-Liang Lu

  5. School of Electrical and Electronic Engineering, University of Manchester, UK

    Hujun Yin

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© 2006 Springer-Verlag Berlin Heidelberg

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Liao, W., Wang, L. (2006). Existence and Global Attractability of Almost Periodic Solution for Competitive Neural Networks with Time-Varying Delays and Different Time Scales. In: Wang, J., Yi, Z., Zurada, J.M., Lu, BL., Yin, H. (eds) Advances in Neural Networks - ISNN 2006. ISNN 2006. Lecture Notes in Computer Science, vol 3971. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11759966_46

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  • DOI: https://doi.org/10.1007/11759966_46

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-34439-1

  • Online ISBN: 978-3-540-34440-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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