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Global convergence of CNNs with neutral type delays and D operator

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Abstract

A model of cellular neural networks with neutral type delays and D operator is proposed. Applying appropriate differential inequality techniques, several sufficient conditions are derived to ensure the global exponential convergence of solutions for the proposed neural networks. Finally, a numerical simulation example is given to illustrate the effectiveness of the obtained results.

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References

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

    Article  MathSciNet  Google Scholar 

  2. Wu J (2001) Introduction to neural dynamics and signal transmission delay. Walter de Gruyter, Belin

    Book  MATH  Google Scholar 

  3. Kwon O, Lee S, Park J (2010) Improved results on stability analysis of neural networks with time-varying delays: novel delay-dependent criteria. Mod Phys Lett B 24:775–789

    Article  MATH  Google Scholar 

  4. Kwon O, Park J (2009) Exponential stability analysis for uncertain neural networks with interval time-varying delays. Appl Math Comput 212:530–541

    MathSciNet  MATH  Google Scholar 

  5. Liu B (2016) Global exponential convergence of non-autonomous cellular neural networks with multi-proportional delays. Neurocomputing 191:352–355

    Article  Google Scholar 

  6. Yao L (2016) Global exponential convergence of neutral type shunting inhibitory cellular neural networks with D operator. Neural Process Lett. doi:10.1007/s11063-016-9529-7

  7. Hale JK, Mawhin J (1975) Coincidence degree and periodic solutions of neutral equations. J Differ Equ 15:295–307

    Article  MathSciNet  MATH  Google Scholar 

  8. Komanovskii VB, Nosov VR (1986) Stability of functional differential equations. Academic Press, London

    Google Scholar 

  9. Kuang Y (1993) Delay differential equations with applications in population dynamical system. Academic Press, New York

    MATH  Google Scholar 

  10. Gui Z, Ge W, Yang X (2007) Periodic oscillation for a Hopfield neural networks with neutral delays. Phys Lett A 364(3–4):267–273

    Article  MATH  Google Scholar 

  11. Xiao B (2009) Existence and uniqueness of almost periodic solutions for a class of Hopfield neural networks with neutral delays. Appl Math Lett 22:528–533

    Article  MathSciNet  MATH  Google Scholar 

  12. Mandal S, Majee NC (2011) Existence of periodic solutions for a class of Cohen–Grossberg type neural networks with neutral delays. Neurocomputing 74(6):1000–1007

    Article  Google Scholar 

  13. Li L, Fang Z, Yang Y (2012) A shunting inhibitory cellular neural network with continuously distributed delays of neutral type. Nonlinear Anal Real World Appl 13:1186–1196

    Article  MathSciNet  MATH  Google Scholar 

  14. Chen Z (2013) A shunting inhibitory cellular neural network with leakage delays and continuously distributed delays of neutral type. Neural Comput Appl 23:2429–2434

    Article  Google Scholar 

  15. Liu B (2015) Pseudo almost periodic solutions for neutral type CNNs with continuously distributed leakage delays. Neurocomputing 148:445–454

    Article  Google Scholar 

  16. Liu X (2015) Exponential convergence of SICNNs with delays and oscillating coefficients in leakage terms. Neurocomputing 168:500–504

    Article  Google Scholar 

  17. Zhao C, Wang Z (2015) Exponential convergence of a SICNN with leakage delays and continuously distributed delays of neutral type. Neural Process Lett 41:239–247

    Article  Google Scholar 

  18. Yu Y (2016) Global exponential convergence for a class of neutral functional differential equations with proportional delays. Meth Appl Sci Math. doi:10.1002/mma.3880

  19. Yu Y (2016) Global exponential convergence for a class of HCNNs with neutral time-proportional delays. Appl Math Comput 285:1–7

    MathSciNet  Google Scholar 

  20. Peng L, Wang L (2014) Periodic solutions for first order neutral functional differential equations with multiple deviating arguments. Ann Polon Math 111(2):197–213

    Article  MathSciNet  MATH  Google Scholar 

  21. Candan T (2016) Existence of positive periodic solutions of first order neutral differential equations with variable coefficients. Appl Math Lett 52:142–148

    Article  MathSciNet  MATH  Google Scholar 

  22. Jiang A (2015) Exponential convergence for shunting inhibitory cellular neural networks with oscillating coefficients in leakage terms. Neurocomputing 165:159–162

    Article  Google Scholar 

  23. Jiang A (2016) Exponential convergence for HCNNs with oscillating coefficients in leakage terms. Neural Process Lett 43:285–294

    Article  Google Scholar 

  24. Zhang H, Liu X, Yang M (2015) Globally exponential stability of a delay reduced SIR model for migrant workers’ home residence. Appl Math Lett 50:119–125

    Article  MathSciNet  MATH  Google Scholar 

  25. Long Z (2016) New results on anti-periodic solutions for SICNNs with oscillating coefficients in leakage terms. Neurocomputing 171(1):503–509

    Article  Google Scholar 

  26. Liu X (2016) Improved convergence criteria for HCNNs with delays and oscillating coefficients in leakage terms. Neural Comput Appl 27:917–925

    Article  Google Scholar 

Download references

Acknowledgments

The author would like to express the sincere appreciation to the editor and reviewer for their helpful comments in improving the presentation and quality of the paper. In particular, the author expresses the sincere gratitude to Prof. Bingwen Liu's help on the proof of Theorem 2.1. Moreover, this work was supported by the National Social Science Fund of China (15BJY122), the Humanities and Social Sciences Foundation of Ministry of Education of P. R. China (Grant No. 12YJAZH173), and the Aid program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Hunan University of Commerce, Changsha, 410205, Hunan, People’s Republic of China

    Luogen Yao

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  1. Luogen Yao
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Correspondence to Luogen Yao.

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Yao, L. Global convergence of CNNs with neutral type delays and D operator. Neural Comput & Applic 29, 105–109 (2018). https://doi.org/10.1007/s00521-016-2403-8

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  • DOI: https://doi.org/10.1007/s00521-016-2403-8

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