On Equilibrium and Stability of a Class of Neural Networks with Mixed Delays

  • Shuyong Li
  • Yumei Huang
  • Daoyi Xu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3971)


In this paper the authors analyze problems of existence and global asymptotic stability of the equilibrium for the neural networks with mixed delays. Some new sufficient conditions ensuring the existence, uniqueness, and global asymptotic stability of the equilibrium are established by means of Leray-Schauder principle, arithmetic-mean-geometric-mean inequality and vector delay differential inequality technique. These conditions are less restrictive than previously known criteria.


Neural Network Unique Equilibrium Cellular Neural Network Global Asymptotic Stability Discrete Delay 


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  1. 1.
    Cao, J.D.: A Set of Stability Criteria for Delayed Cellular Neural Networks. IEEE Trans. Circuits Syst. I 48, 494–498 (2001)MATHCrossRefGoogle Scholar
  2. 2.
    Guo, S., Huang, L.: Exponential Stability and Periodic Solutions of Neural Networks with Continuously Distributed Delays. Phys. Rev. E 67, 11902 (2003)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Kolmanovskii, V., Myshkis, A.: Intoduction to the Theory and Applications of Functional Differential Equations. Kluwer Academic Publishers, Dordrecht (1999)Google Scholar
  4. 4.
    Zeidler, E.: Nonlinear Functional Analysis and its Application. Springer, New York (1986)Google Scholar
  5. 5.
    Beckenbach, E.F., Bellman, R.: Inequalities. Springer, New York (1961)Google Scholar
  6. 6.
    Berman, A., Plemmons, R.J.: Nonnegative Matrices in the Mathematical Sciences. Academic Press, New York (1979)MATHGoogle Scholar
  7. 7.
    Xu, D.Y.: Integro-Differential Equations and Delay Integral Inequalities. Tohoku Math. J. 44, 365–378 (1992)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Shuyong Li
    • 1
  • Yumei Huang
    • 2
    • 3
  • Daoyi Xu
    • 2
  1. 1.College of Mathematics and Software ScienceSichuan Normal UniversityChengduChina
  2. 2.Institute of MathematicsSichuan UniversityChengduChina
  3. 3.School of Mathematics and Computer EngineeringXihua universityPixianChina

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