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Universal Approach to Study Delayed Dynamical Systems

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Advances in Natural Computation (ICNC 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3610))

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Abstract

In this paper, we propose a universal approach to study dynamical behaviors of various neural networks with time-varying delays. A universal model is proposed, which includes most of the existing models as special cases. An effective approach, which was first proposed in [1] , to investigate global stability is given, too. It is pointed out that the approach proposed in the paper [1] applies to the systems with time-varying delays, too.

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References

  1. Chen, T.: Global Exponential Stability of Delayed Hopfield Neural Networks. Neural Networks 14(8), 977–980 (2001)

    Article  Google Scholar 

  2. Liao, X., Wang, J.: Algebraic Criteria for Global Exponential Stability of Cellular Neural Networks With multiple Time Delays. IEEE Tran. on Circuits and Systems-I 50(2), 268–275 (2003)

    Article  MathSciNet  Google Scholar 

  3. Lu, H., Chung, F.-L., He, Z.: Some sufficient conditions for global exponential stability of delayed Hopfield neural networks. Neural Networks 17, 537–544 (2004)

    Article  MATH  Google Scholar 

  4. Zeng, Z., Wang, J., Liao, X.: Global Exponential Stability of a General Class of Recurrent Neural Networks With Time-Varying Delays. IEEE Tran. on Circuits and Systems-I 50(10), 1353–1358 (2003)

    Article  MathSciNet  Google Scholar 

  5. Zhang, J.: Globally Exponential Stability of Neural Networks With varying Delays. IEEE Tran. on Circuits and Systems-I 50(2), 288–291 (2003)

    Article  Google Scholar 

  6. Yi, Z.: Global exponential convergence of recurrent neural networks with variable delays. Theor. Comput. Sci. 312, 281–293 (2004)

    Article  MATH  Google Scholar 

  7. Huang, H., Ho, D.W.C., Cao, J.: Analysis of global exponential stability and periodic solutions of neural networks with time-varying delays. Neural Networks 18(2), 161–170 (2005)

    Article  Google Scholar 

  8. Huang, H., Cao, J.: On global symptotic stability of recurrent neural networks with time-varying delays. Applied Mathematics and Computation 142, 143–154 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  9. Cao, J., Wang, J.: Global Asymptotic Stability of a General Class of Recurrent Neural Networks With Time-Varying Delays. IEEE Tran. on Circuits and Systems-I 50(1), 34–44 (2003)

    Article  MathSciNet  Google Scholar 

  10. Cao, J., Wang, J.: Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delays. Neural Networks 17, 379–390 (2004)

    Article  MATH  Google Scholar 

  11. Peng, J., Qiao, H., Xu, Z.-b.: A new approach to stability of neural networks with time-varying delays. Neural Networks 15, 95–103 (2002)

    Article  Google Scholar 

  12. Chen, T., Lu, W., Chen, G.: Dynamical Behaviors of a Large Class of General Delayed Neural Networks. Neural Computation 17(4), 949–968 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  13. Hu, S., Liu, D.: On the global output convergence of a class of recurrent neural networks with time-varying inputs. Neural Networks 18(2), 171–178 (2005)

    Article  MATH  Google Scholar 

  14. Gopalsamy, K., He, X.: Stability in Asymmetric Hopfield Nets with Transmission Delays. Phys. D. 76, 344–358 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  15. Zhao, H.: Global stability of neural networks with distributed delays. Physical Review E 68, 051909 (2003)

    Article  Google Scholar 

  16. Zhang, Q., Wei, X., Xu, J.: Global exponential stability of Hopfield neural networks with continuous distributed delays. Physics Letters A 315, 431–436 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  17. Zhao, H.: Global asymptotic stability of Hopfield neural network involving distributed delays. Neural Networks 17, 47–53 (2004)

    Article  MATH  Google Scholar 

  18. Jiang, H., Teng, Z.: Global exponential stability of cellular neural networks with time-varying coefficients and delays. Neural Networks 17, 1415–1425 (2004)

    Article  MATH  Google Scholar 

  19. Zhang, J.: Absolutely exponential stability of a class of neural networks with unbounded delay. Neural Networks 17, 391–397 (2004)

    Article  MATH  Google Scholar 

  20. Zheng, Y., Chen, T.: Global exponential stability of delayed periodic dynamical systems. Physics Letters A 322(5-6), 344–355 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  21. Lu, W., Chen, T.: On Periodic Dynamical Systems. Chinese Annals of Mathematics Series B 25B(4), 455–462 (2004)

    Article  MathSciNet  Google Scholar 

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© 2005 Springer-Verlag Berlin Heidelberg

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Chen, T. (2005). Universal Approach to Study Delayed Dynamical Systems. In: Wang, L., Chen, K., Ong, Y.S. (eds) Advances in Natural Computation. ICNC 2005. Lecture Notes in Computer Science, vol 3610. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11539087_30

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  • DOI: https://doi.org/10.1007/11539087_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28323-2

  • Online ISBN: 978-3-540-31853-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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