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Existence and stability of almost periodic solutions for CNNs with continuously distributed leakage delays

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Abstract

In this paper, a class of nonlinear nonautonomous cellular neural networks system with the introduction of continuously distributed delays in the leakage (or forgetting) terms is considered. By using Lyapunov functional method and differential inequality techniques, without assuming the boundedness on the activation functions, we derive a set of easily verifiable sufficient conditions that guarantee the existence and exponential stability of almost periodic solutions for the system. Moreover, an example and its numerical simulation are given to demonstrate the feasibility of our method.

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References

  1. Chua LO, Yang L (1988) Cellular neural networks: theory. IEEE Trans Circuits Syst 35:1257–1272

    Article  MATH  MathSciNet  Google Scholar 

  2. Chua LO, Yang L (1988) Cellular neural networks: application. IEEE Trans Circuits Syst 35:1273–1290

    Article  MathSciNet  Google Scholar 

  3. Chua LO, Roska T (1990) Cellular neural networks with nonlinear and delay-type template elements. In: Proceedings of 1990 IEEE international workshop on cellular neural networks and their applications, pp 12–25

  4. Park JH (2006) Further result on asymptotic stability criterion of cellular neural networks with time-varying discrete and distributed delays. Appl Math Comput 182:1661–1666

    Article  MATH  MathSciNet  Google Scholar 

  5. Li X, Ding C, Zhu Q (2010) Synchronization of stochastic perturbed chaotic neural networks with mixed delays. J Franklin Inst 347:1266–1280

    Article  MATH  MathSciNet  Google Scholar 

  6. Kwon O, Park J (2008) Delay-dependent stability for uncertain cellular neural networks with discrete and distribute time-varying delays. J Franklin Inst 345:766–778

    Article  MATH  MathSciNet  Google Scholar 

  7. Wang L (2005) Stability of Cohen-Grossberg neural networks with distributed delays. Appl Math Comput 160:93–110

    Article  MATH  MathSciNet  Google Scholar 

  8. He CY (1992) Almost periodic differential equation. Higher Education Publishing House, Beijing, pp 90–100 (In Chinese)

  9. Fink AM (1974) Almost periodic differential equations. Lecture Notes in Mathematics, vol 377. Springer, Berlin

  10. Liu B (2007) Almost periodic solutions for Hopfield neural networks with continuously distributed delays. Math Comput Simul 73(5):327–335

    Article  MATH  Google Scholar 

  11. Liu B, Huang L (2006) Existence and stability of almost periodic solutions for shunting inhibitory cellular neural networks with continuously distributed delays. Phys Lett A 349(1–4):177–186

    Article  Google Scholar 

  12. Liu B, Huang L (2007) Existence and exponential stability of almost periodic solutions for cellular neural networks with mixed delays. Chaos Solitons Fractals 32(1):95–103

    Article  MATH  MathSciNet  Google Scholar 

  13. Liu B, Huang L (2008) Positive almost periodic solutions for recurrent neural networks. Nonlinear Anal Real World Appl 9:830–841

    Article  MATH  MathSciNet  Google Scholar 

  14. Lu W, Chen T (2005) Global exponential stability of almost periodic solutions for a large class of delayed dynamical systems. Sci China Ser A Math 8(48):1015–1026

    Article  Google Scholar 

  15. Xiang H, Cao J (2009) Almost periodic solutions of recurrent neural networks with continuously distributed delays. Nonlinear Anal 71(12):6097–6108

    Article  MATH  MathSciNet  Google Scholar 

  16. Zhou J, Zhao W, Lv X, Zhu H (2011) Stability analysis of almost periodic solutions for delayed neural networks without global Lipschitz activation functions. Math Comput Simul 81(11):2440–2455

    Article  MATH  MathSciNet  Google Scholar 

  17. Haykin S (1994) Neural networks. Prentice-Hall, NJ

    MATH  Google Scholar 

  18. Kosok B (1992) Neural networks and fuzzy systems. Prentice-Hall, NewDelhi

    Google Scholar 

  19. Gopalsamy K (1992) Stability and oscillations in delay differential equations of population dynamics. Kluwer, Dordrecht

    Book  MATH  Google Scholar 

  20. Gopalsamy K (2007) Leakage delays in BAM. J Math Anal Appl 325:1117–1132

    Article  MATH  MathSciNet  Google Scholar 

  21. Li X, Cao J (2010) Delay-dependent stability of neural networks of neutral type with time delay in the leakage term. Nonlinearity 23:1709–1726

    Article  MATH  MathSciNet  Google Scholar 

  22. Li X, Rakkiyappan R, Balasubramaniam P (2011) Existence and global stability analysis of equilibrium of fuzzy cellular neural networks with time delay in the leakage term under impulsive perturbations. J Franklin Inst 348:135–155

    Article  MATH  MathSciNet  Google Scholar 

  23. Chen Z, Meng J (2012) Exponential convergence for cellular neural networks with time-varying delays in the leakage terms. Hindawi Publishing Corporation. Abstr Appl Anal ID 941063: 11. doi:10.1155/2012/941063

  24. Liu B (2013) Global exponential stability for BAM neural networks with time-varying delays in the leakage terms. Nonlinear Anal Real World Appl 14:559–566

    Article  MATH  MathSciNet  Google Scholar 

  25. Gan Q, Liang Y (2012) Synchronization of chaotic neural networks with time delay in the leakage term and parametric uncertainties based on sampled-data control. J Franklin Inst 349(6):1955–1971

    Article  MathSciNet  Google Scholar 

  26. Peng S (2010) Global attractive periodic solutions of BAM neural networks with continuously distributed delays in the leakage terms. Nonlinear Anal Real World Appl 11:2141–2151

    Article  MATH  MathSciNet  Google Scholar 

  27. Hino Y, Murakami S, Nai T (1991) Functional differential equations with infinite delay. Lecture in mathematics, vol 1473. Springer, Berlin

Download references

Acknowledgments

I wish to thank the reviewers for their valuable comments that led to truly significant improvement of the manuscript. This work was supported by the Natural Scientific Research Fund of Hunan Provincial of PR China (Grant No. 11JJ6006), and the Natural Scientific Research Fund of Hunan Provincial Education Department of PR China (Grant Nos. 11C0916, 11C0915).

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  1. College of Mathematics and Computer Science, Hunan University of Arts and Science, Changde, Hunan, 415000, China

    Hong Zhang

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  1. Hong Zhang
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Correspondence to Hong Zhang.

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Zhang, H. Existence and stability of almost periodic solutions for CNNs with continuously distributed leakage delays. Neural Comput & Applic 24, 1135–1146 (2014). https://doi.org/10.1007/s00521-012-1336-0

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  • DOI: https://doi.org/10.1007/s00521-012-1336-0

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