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Convergence of Neutral Type Fuzzy Cellular Neural Networks with D Operator

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Abstract

A model of neutral type fuzzy cellular neural networks with D operator is proposed. Applying 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. Yang T, Yang L, Wu C, Chua L (1996) Fuzzy cellular neural networks: theory. In: Proceedings of IEEE international work shop on cellular neural networks and applications, pp 181–186

  2. Yang T, Yang L, Wu C, Chua L (1996) Fuzzy cellular neural networks: applications. In: Proceedings of IEEE international work shop on cellular neural networks and applications, pp 225–230

  3. Abdurahman A, Jiang H, Teng Z (2016) Finite-time synchronization for fuzzy cellular neural networks with time-varying delays. Fuzzy Sets Syst 297:96–111

    Article  MathSciNet  MATH  Google Scholar 

  4. Jia R (2017) Finite-time stability of a class of fuzzy cellular neural networks with multi-proportional delays. Fuzzy Sets Syst 319(15):70–80

    Article  MathSciNet  MATH  Google Scholar 

  5. Jian J, Jiang W (2015) Lagrange exponential stability for fuzzy Cohen–Grossberg neural networks with time-varying delays. Fuzzy Sets Syst 277:65–80

    Article  MathSciNet  MATH  Google Scholar 

  6. Zheng C, Zhang X, Wang Z (2015) Mode-dependent stochastic stability criteria of fuzzy Markovian jumping neural networks with mixed delays. ISA Trans 56:8–17

    Article  Google Scholar 

  7. Kao Y, Shi L, Xie J, Karimi H (2015) Global exponential stability of delayed Markovian jump fuzzy cellular neural networks with generally incomplete transition probability. Neural Netw 63:18–30

    Article  MATH  Google Scholar 

  8. Yang G (2014) New results on the stability of fuzzy cellular neural networks with time-varying leakage delays. Neural Comput Appl 25(7):1709–1715

    Article  Google Scholar 

  9. Huang Z (2017) Almost periodic solutions for fuzzy cellular neural networks with time-varying delays. Neural Comput Appl 28:2313–2320

    Article  Google Scholar 

  10. Huang Z (2017) Almost periodic solutions for fuzzy cellular neural networks with multi-proportional delays. Int J Mach Learn Cybern 8:1323–1331

    Article  Google Scholar 

  11. Muralisankar S, Gopalakrishnan N, Balasubramaniam P (2011) Robust exponential stability criteria for TCS fuzzy stochastic delayed neural networks of neutral type. Circ Syst Signal Process 30(30):1617–1641

    Article  MATH  Google Scholar 

  12. Balasubramaniam P, Vembarasan V (2011) Robust stability of uncertain fuzzy BAM neural networks of neutral-type with Markovian jumping parameters and impulses. Comput Math Appl 62(4):1838–1861

    Article  MathSciNet  MATH  Google Scholar 

  13. Park MJ, Kwon OM, Park JuH, Lee SM (2012) Simplified stability criteria for fuzzy Markovian jumping Hopfield neural networks of neutral type with interval time-varying delays. Expert Syst Appl 39(5):5625–5633

    Article  Google Scholar 

  14. Muralisankar S, Gopalakrishnan N (2014) Robust stability criteria for Takagi–Sugeno fuzzy Cohen–Grossberg neural networks of neutral type. Neurocomputer 144(1):516–525

    Article  MATH  Google Scholar 

  15. Sathy R, Balasubramaniam P (2012) Direct delay decomposition approach to robust stability on fuzzy Markov-type BAM neural networks with time-varying delays. In: Mathematical modelling and scientific computation, Springer, Berlin, pp 245–254

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

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

    MATH  Google Scholar 

  19. Yao L (2017) Global exponential convergence of neutral type shunting inhibitory cellular neural networks with D operator. Neural Process Lett 45:401–409

    Article  Google Scholar 

  20. Yao L (2018) Global convergence of CNNs with neutral type delays and \(D\) operator. Neural Comput Appl. 29:105–109

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  24. 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 

  25. 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 

  26. Liu B (2017) Finite-time stability of CNNs with neutral proportional delays and time-varying leakage delays. Math Methods Appl Sci 40:167–174

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  28. 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 

  29. Yu Y (2016) Global exponential convergence for a class of neutral functional differential equations with proportional delays. Math Methods Appl Sci 39:4520–4525

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  31. Yang G (2017) New results on convergence of fuzzy cellular neural networks with multi-proportional delays. Int J Mach Learn Cybern. https://doi.org/10.1007/s13042-017-0672-x

  32. Yang G, Wang W (2017) New results on convergence of CNNs with neutral type proportional delays and D operator. Neural Process Lett. https://doi.org/10.1007/s11063-018-9818-4

  33. Huang C, Cao J (2016) Stability analysis of switched cellular neural networks: a mode-dependent average dwell time approach. Neural Netw 82:84–99

    Article  Google Scholar 

  34. Huang C, Cao J (2011) Convergence dynamics of stochastic Cohen–Grossberg neural networks with unbounded distributed delays. IEEE Trans Neural Netw 22:561–572

    Article  Google Scholar 

  35. Huang C, Cao J (2010) On pth moment exponential stability of stochastic Cohen–Grossberg neural networks with time-varying delays. Neurocomputer 73:986–990

    Article  Google Scholar 

Download references

Acknowledgements

I am extremely grateful to the anonymous reviewer and the editor for their valuable comments and suggestions which have contributed considerably to the improved presentation of this paper. This work was supported by Natural Scientific Research Fund of Hunan Provincial of China (Grant Nos. 2015JJ5011, 2018JJ2372, 2018JJ2087), a Key Project Supported by Scientific Research Fund of Hunan Provincial Education Department (15A038) and Natural Scientific Research Fund of Hunan Provincial Education Department of China (Grant No. 17C1076).

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Correspondence to Zhibin Chen.

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Chen, Z. Convergence of Neutral Type Fuzzy Cellular Neural Networks with D Operator. Neural Process Lett 49, 1189–1199 (2019). https://doi.org/10.1007/s11063-018-9864-y

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