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Global Asymptotic Stability of Cellular Neutral Networks With Variable Coefficients and Time-Varying Delays

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Advances in Neural Networks – ISNN 2007 (ISNN 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4491))

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Abstract

In this paper, we study the global asymptotic stability properties of cellular neural networks with variable coefficients and time varying delays. We present sufficient conditions for the global asymptotic stability of the neural networks . The proposed conditions, which are applicable to all continuous nonmonotonic neuron activation functions and do not require the interconnection matrices to be symmetric, establish the relationships between network parameters of the neural systems and the delay parameters. Some examples show that our results are new and improve the previous results derived in the literature.

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References

  1. Roska, T., Boros, T., Thiran, P., Chua, L.O.: Detecting Simple Motion Using Celluar Neural Networks. In: Proc. IEEE int. workshop on Celluar Neural Networks and Their Applications, pp. 127–138 (1990)

    Google Scholar 

  2. Arik, S.: Global Asymptotic Stability of A Class of dynamical Neural Networks. IEEE Trans. Circuits Syst. I 47(4), 568–571 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  3. Arik, S., Tavsanoglu, V.: Equilibrium Analysis of Delayed CNNs. IEEE Trans. Circuits Syst. I 2, 168–171 (1998)

    Article  MATH  Google Scholar 

  4. Forti, M., Tesi, A.: New Conditions for Global Stability of Neural Networks with Applicatons to Linear and Quadractic Programming Problems. IEEE Trans. Circuits Syst. I 7, 354–365 (1995)

    Article  MATH  Google Scholar 

  5. Gao, J.: Exponential Stability and Periodic Oscillatory Solution in BAM Networks with Delays. IEEE Trans. Neural Networks 2, 457–463 (2002)

    Google Scholar 

  6. Gao, J., Wang, J.: Global Asymptotic Stability of a General Class of Recurrent Neural Networks with Time-Varying Delays. IEEE Trans. Circuits Syst. I 1, 34–44 (2003)

    MathSciNet  Google Scholar 

  7. Lu, H., Chung, F.L., He, Z.: Some Sufficient Conditions for Global Exponential Stability of Delayed Neural Networks. Neural Networks, 437–544 (2004)

    Google Scholar 

  8. Zhang, Q., Ma, R., Wang, C., Xu, J.: On the Global Stability of Delayed Neural Networks. IEEE Trans. Autom. Control 5, 794–797 (2003)

    Article  Google Scholar 

  9. Chen, T.: Global Conbergence of Delayed Dynamical Systems. IEEE Trans. Neural Networks 6, 1532–1536 (2001)

    Article  Google Scholar 

  10. Ensari, T., Arik, S.: Global Stability Analysis of Neural Networks with Multiple Time Varying Delays. IEEE Trans. Autom. Control 11, 1781–1785 (2005)

    Article  MathSciNet  Google Scholar 

  11. Zeng, Z., Wang, J., Liao, X.: Global Exponential Stability of A General Class of Recurrent Neural Networks with Unbounded Time-Varying Delays. IEEE Transactions on Circuits and Systems-Part II Express Briefs 52(3), 168–173 (2005)

    Article  Google Scholar 

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

    MathSciNet  Google Scholar 

  13. Hu, S., Wang, J.: Global Robust Stability of A Class of Discrete-Time Interval Neural Networks. IEEE Transactions on Circuits and Systems–Part I: Regular Papers 53, 129–138 (2006)

    Article  MathSciNet  Google Scholar 

  14. Zeng, Z., Wang, J.: Complete Stability of Cellular Neural Networks with Time-Varying Delays. IEEE Transactions on Circuits and Systems-Part I: Regular Papers 53, 944–955 (2006)

    Article  MathSciNet  Google Scholar 

  15. Liao, X., Wang, J., Zeng, Z.: Global Asymptotic Stability and Global Exponential Stability of Delayed Cellular Neural Networks. IEEE Transactions on Circuits and Systems-Part II Express Briefs 52(7), 403–409 (2005)

    Article  Google Scholar 

  16. Horn, R.A., Johnson, C.R.: Topic in Matrix Analysis. Cambridge Univ. Press, Cambridge (1991)

    Book  Google Scholar 

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Author information

Authors and Affiliations

  1. College of Information Science and Engineering, Ocean University of China, China

    Yonggui Kao & Lijing Zhang

  2. Department of Mathematics, Ocean University of China, Qingdao 266071, China

    Cunchen Gao

  3. Department of Mathematics, ZaoZhuang University , ZaoZhuang 277160, China

    Yonggui Kao

Authors
  1. Yonggui Kao
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  2. Cunchen Gao
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  3. Lijing Zhang
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering (M/C 154), University of Illinois at Chicago, 851 S. Morgan Street, 60607-7053, Chicago, IL, USA

    Derong Liu

  2. School of Automation, Southeast University, 210096, Nanjing, China

    Shumin Fei

  3. Laboratory of Complex Systems, Institute of Automation, Chinese Adacemy of Sciences, 100080, Beijing, P. R. China

    Zeng-Guang Hou

  4. School of Information Science and Engineering, Northeast University, Shenyang, 110004, China

    Huaguang Zhang

  5. School of Electrical Engineering, Hohai University, Nanjing, 210098, China

    Changyin Sun

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© 2007 Springer-Verlag Berlin Heidelberg

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Kao, Y., Gao, C., Zhang, L. (2007). Global Asymptotic Stability of Cellular Neutral Networks With Variable Coefficients and Time-Varying Delays. In: Liu, D., Fei, S., Hou, ZG., Zhang, H., Sun, C. (eds) Advances in Neural Networks – ISNN 2007. ISNN 2007. Lecture Notes in Computer Science, vol 4491. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72383-7_106

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  • DOI: https://doi.org/10.1007/978-3-540-72383-7_106

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72382-0

  • Online ISBN: 978-3-540-72383-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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