Neural Processing Letters

, Volume 39, Issue 2, pp 167–177

New Results on Exponential Convergence for HRNNs with Continuously Distributed Delays in the Leakage Terms

Article

Abstract

This paper concerns with exponential convergence for a class of high-order recurrent neural networks with continuously distributed delays in the leakage terms. Without assuming the boundedness on the activation functions, some sufficient conditions are derived to ensure that all solutions of the networks converge exponentially to the zero point by using Lyapunov functional method and differential inequality techniques, which correct some recent results of Chen and Yang (Neural Comput Appl. doi:10.1007/s00521-012-1172-2, 2012). Moreover, we propose a new approach to prove the exponential convergence of HRNNs with continuously distributed leakage delays.

Keywords

High-order recurrent neural networks Exponential convergence  Continuously distributed delay Leakage term 

Mathematics Subject Classification (2000)

34C25 34K13 34K25 

References

  1. 1.
    Balasubramaniam P, Vembarasan V, Rakkiyappan R (2012) Global robust asymptotic stability analysis of uncertain switched Hopfield neural networks with time delay in the leakage term. Neural Comput Appl 21(7):1593–1616CrossRefGoogle Scholar
  2. 2.
    Long S, Song Q, Wang X, Li D (2012) Stability analysis of fuzzy cellular neural networks with time delay in the leakage term and impulsive perturbations. J Frankl Inst 349(7):2461–2479CrossRefMathSciNetGoogle Scholar
  3. 3.
    Li X, Cao J (2010) Delay-dependent stability of neural networks of neutral type with time delay in the leakage term. Nonlinearity 23(7):1709–1726CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Lakshmanan S, Park JH, Jung HY, Balasubramaniam P (2012) Design of state estimator for neural networks with leakage, discrete and distributed delays. Appl Math Comput 218(22):11297–11310CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Gopalsamy K (2007) Leakage delays in BAM. J Math Anal Appl 325:1117–1132CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Park MJ, Kwon OM, Park JuH, Lee SM, Cha EJ (2012) Synchronization criteria for coupled neural networks with interval time-varying delays and leakage delay. Appl Math Comput 218(12):6762–6775CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Balasubramaniam P, Vembarasan V, Rakkiyappan R (2011) Leakage delays in TS fuzzy cellular neural networks. Neural Process Lett 33(2):111–136CrossRefGoogle Scholar
  8. 8.
    Chen Z, Meng J (2012) Exponential convergence for cellular neural networks with time-varying delays in the leakage terms. Abstr Appl Anal. doi:10.1155/2012/941063
  9. 9.
    Dembo A, Farotimi O, Kailath T (1991) High-order absolutely stable neural networks. IEEE Trans Circuits Syst 38:57–65CrossRefMATHGoogle Scholar
  10. 10.
    Psaltis D, Park CH, Hong J (1988) Higher order associative memories and their optical implementations. Neural Netw 1:143–163CrossRefGoogle Scholar
  11. 11.
    Karayiannis NB, Venetsanopoulos AN (1995) On the training and performance of high-order neural networks. Math Biosci 129(2):143–168CrossRefMATHGoogle Scholar
  12. 12.
    Yi X, Shao J, Yu Y, Xiao B (2008) New convergence behavior of high-order Hopfield neural networks with time-varying coefficients. J Comput Appl Math 219:216–222CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Shao J (2009) Global exponential convergence for delayed cellular neural networks with a class of general activation functions. Nonlinear Anal Real World Appl 10:1816–1821CrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    Huang Z, Peng L, Xu X (2010) Anti-periodic solutions for high-order cellular neural networks with time-varying delays. Electron J Differ Equ 59:1–9Google Scholar
  15. 15.
    Zhang H, Wang W, Xiao B (2011) Exponential convergence for high-order recurrent neural networks with a class of general activation functions. Appl Math Model 35:123–129CrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    Wang Y, Lu C, Ji G, Wang L (2011) Global exponential stability of high-order Hopfield-type neural networks with S-type distributed time delays. Commun Nonlinear Sci Numer Simul 16(8):3319–3325CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    Nie X, Huang Z (2012) Multistability and multiperiodicity of high-order competitive neural networks with a general class of activation functions. Neurocomputing 82(1):1–13CrossRefGoogle Scholar
  18. 18.
    Liu Q, Xu R (2011) Periodic solutions of high-order Cohen–Grossberg neural networks with distributed delays. Commun Nonlinear Sci Numer Simul 16(7):2887–2893CrossRefMATHMathSciNetGoogle Scholar
  19. 19.
    Chen Z, Yang M (2012) Exponential convergence for HRNNs with continuously distributed delays in the leakage terms. Neural Comput Appl. doi:10.1007/s00521-012-1172-2
  20. 20.
    Zhang H (2013) Existence and stability of almost periodic solutions for CNNs with continuously distributed leakage delays. Neural Comput Appl. doi:10.1007/s00521-012-1336-0
  21. 21.
    Zhang H, Yang M (2013) Global exponential stability of almost periodic solutions for SICNNs with continuously distributed leakage delays. Abstr Appl Anal. doi:10.1155/2013/307981

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.College of Mathematics and Computer ScienceHunan University of Arts and ScienceChangdePeople’s Republic of China
  2. 2.College of EngineeringZhejiang Normal UniversityJinhuaPeople’s Republic of China

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