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Existence and Stability of Periodic Solutions for BAM Neural Networks with Time-Varying Delays and Impulses

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Advances in Neural Networks – ISNN 2009 (ISNN 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5551))

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Abstract

By using the continuation theorem of Mawhin’s coincidence degree theory, some new sufficient conditions are obtained for the existence and stability of periodic solution of BAM neural networks with variable delays and impulses, and without requirement of the boundedness of the activation functions.

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References

  1. Bainov, D.D., Simeonov, P.S.: Stability Theory of Differential Equations with Impulse Effects: Theory and Applications. Ellis Horwood, Chichester (1989)

    MATH  Google Scholar 

  2. Gaines, R.E., Mawhin, J.L.: Coincidence Degree and Nonlinear Differential Equations. Springer, New York (1977)

    Book  MATH  Google Scholar 

  3. Gopalsamy, K., He, X.Z.: Delay-independent Stability in Bi-directional Associative Memory Networks. IEEE Trans Neural Networks 5, 998–1002 (1994)

    Article  Google Scholar 

  4. Guan, Z.H., Chen, G.: On Delayed Impulsive Hopfield Neural Networks. Neural Networks 12, 273–280 (1999)

    Article  Google Scholar 

  5. Gui, Z.J., Ge, W.G.: Existence and Uniqueness of Periodic Solutions of Nonautonomous Cellular Neural Networks with Impuises. Phys. Lett. A 354, 84–94 (2006)

    Article  MATH  Google Scholar 

  6. Gui, Z.J., Yang, X.S., Ge, W.G.: Periodic Solution for Nonautonomous Bidirectional Associative Memory Neural Networks with Impulses. Neurocomputing 70, 2517–2527 (2007)

    Article  Google Scholar 

  7. Ho, W.C., Liang, J.L., James, L.: Global Exponential Stability of Impulsive High-order BAM Neural Networks with Time-varying Delays. Neural Networks 19, 1581–1590 (2006)

    Article  MATH  Google Scholar 

  8. Kosko, B.: Adaptive Bi-directional Associative Memoried. Appl. Optim. 26, 4947–4960 (1987)

    Article  Google Scholar 

  9. Li, Y.K.: Existence and Stability of Periodic Solutions for Cohen-Grossberg Neural Networks with Multiple Delays. Chaos, Solitons and Fractals 20, 459–466 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. Li, Y.: Global Exponential Stability of BAM Neural Networks with Delays and Impulses. Chaos, Solitons and Fractals 24, 279–285 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  11. Li, Y.K., Lu, L.: Global Exponential Stability and Existence of Periodic Solution of Hopfield-type Neural Networks with Impulses. Phys. Lett. A 333, 62–71 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  12. Liu, B.W., Huang, L.H.: Existence and Exponential Stability of Periodic Solutions for a Class of Cohen-Grossberg Neural Networks with Time-varying Delays. Chaos Solitons and Fractals 32, 617–627 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  13. Liu, Z.G., Chen, A., Cao, J.D., Huang, L.H.: Existence and Global Exponential Stability of Periodic Solution for BAM Neural Networks with Periodic Coefficients and Time-varying Delays. IEEE Trans. Circuits Syst. I 50, 1162–1173 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  14. Mohamad, S.: Global Exponential Stability in Continuous-time and Discrete-time Delayed Bidirectional Neural Networks. Physica D 159, 233–251 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  15. Xie, W., Wen, C., Li, Z.: Impulsive Control for the stabilization and synchronization of Lorenz systems. Phys. Lett. A 275, 67–72 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  16. Yang, T., Chua, L.O.: Impulsive Stabilization for Control and Synchronizatin of Chaotic Systems: Theory and Application to Secure Communication. IEEE Trans Circuits and Systems—I 44, 976–988 (1997)

    Article  Google Scholar 

  17. Yang, Z.C., Xu, D.Y.: Existence and Exponential Stability of Periodic Solution for Impulsive Delay Differential Equations and Applications. Nonlinear Analysis 64, 130–145 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  18. Zhu, W., Xu, D.Y.: Global Exponential Stability of Fuzzy Cellular Neural Networks with Impulses and Infinite Delays. Journal of Math R E 28, 1–10 (2008)

    MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Applied Mathematics, Naval Aeronautical and Astronautical University, Yantai, Shandong, 264001, P R China

    Chunxue Wu & Bao Shi

  2. School of Mathematics and Information, Yantai University, Yantai, Shandong, 264005, P R China

    Chunxue Wu

Authors
  1. Chunxue Wu
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  2. Bao Shi
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Editor information

Editors and Affiliations

  1. Departamento de Control Automático, CINVESTAV-IPN, A.P. 14-740, Av.IPN 2508, 07360, México D.F., México

    Wen Yu

  2. Deptartment of Electrical and Computer Engineering, Stevens Institute of Technology, NJ 07030, Hoboken, USA

    Haibo He

  3. Dept. of Electrical and Computer Engineering, South Dakota School of Mines & Technology, 501 E. St. Joseph Street, Rapid City, SD 57701, USA

    Nian Zhang

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© 2009 Springer-Verlag Berlin Heidelberg

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Wu, C., Shi, B. (2009). Existence and Stability of Periodic Solutions for BAM Neural Networks with Time-Varying Delays and Impulses. In: Yu, W., He, H., Zhang, N. (eds) Advances in Neural Networks – ISNN 2009. ISNN 2009. Lecture Notes in Computer Science, vol 5551. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01507-6_55

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  • DOI: https://doi.org/10.1007/978-3-642-01507-6_55

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-01506-9

  • Online ISBN: 978-3-642-01507-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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