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Adaptive synchronization of different Cohen–Grossberg chaotic neural networks with unknown parameters and time-varying delays

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Abstract

In this paper, an adaptive linear feedback controller is presented to study the synchronization problem of different Cohen–Grossberg neural networks with unknown parameters and time-varying delays. Lyapunov stability theory and Barbalat’s lemma are used to guarantee the response system can be synchronized with the drive system. The synchronization criteria of this paper which do not solve any linear matrix inequality are easily verified. These results remove some restrictions on amplification functions and activation functions. Finally, numerical simulations are carried out to illustrate the effectiveness of the obtained results.

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References

  1. Cohen, M.A., Grossberg, S.: Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans. Syst. Man Cybern. 13, 815–826 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  2. Hopfield, J.J.: Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. USA 79, 2554–2558 (1982)

    Article  MathSciNet  Google Scholar 

  3. Chen, Z., Yang, H.: Complete synchronization for impulsive Cohen–Grossberg neural networks with delay under noise perturbation. Chaos Solitons Fractals 42, 1664–1669 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  4. Li, T., Song, A., Fei, S.: Synchronization control for arrays of coupled discrete-time delayed Cohen–Grossberg neural networks. Neurocomputing 74, 197–204 (2010)

    Article  Google Scholar 

  5. Yu, J., Hu, C., Jiang, H., Teng, Z.: Exponential synchronization of Cohen–Grossberg neural networks via periodically intermittent control. Neurocomputing 4, 1776–1782 (2011)

    Article  Google Scholar 

  6. Zhu, Q., Cao, J.: Adaptive synchronization of chaotic Cohen–Crossberg neural networks with mixed time delays. Nonlinear Dyn. 61, 517–534 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  7. Zhu, Q.X., Cao, J.D.: The pth moment exponential synchronization for stochastic delayed Cohen–Grossberg neural networks with Markovian switching. Nonlinear Dyn. 67, 829–845 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  8. He, W., Cao, J.: Adaptive synchronization of a class of chaotic neural networks with known or unknown parameters. Phys. Lett. A 372, 408–416 (2008)

    Article  MATH  Google Scholar 

  9. Ma, T.D., Fu, J.: On the exponential synchronization of stochastic impulsive chaotic delayed neural networks. Neurocomputing 74, 857–862 (2011)

    Article  Google Scholar 

  10. Gan, Q.T.: Adaptive synchronization of Cohen–Grossberg neural networks with unknown parameters and mixed time-varying delays. Commun. Nonlinear Sci. Numer. Simul. 17, 3040–3049 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  11. Zhou, W.N., Tong, D.B., Fang, J.A., Zhu, Q.Y.: Adaptive synchronization for stochastic neural networks of neutral-type with mixed time-delays. Neurocomputing 99, 477–485 (2013)

    Article  Google Scholar 

  12. Carroll, T.L., Pecora, L.M.: Synchronization chaotic circuits. IEEE Trans. Circuits Syst. 38(4), 453–456 (1991)

    Article  Google Scholar 

  13. Fu, J., Zhang, H.G., Ma, T.D., Zhang, Q.L.: On passivity analysis for stochastic neural networks with interval time-varying delay. Neurocomputing 73, 795–801 (2010)

    Article  Google Scholar 

  14. Odibat, Z.M.: Adaptive feedback control and synchronization of nonidentical chaotic fractional order systems. Nonlinear Dyn. 60, 479–487 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  15. Zhang, H.G., Ma, T.D., Huang, G.B., Wang, Z.L.: Robust global exponential synchronization of uncertain chaotic delayed neural networks via dual-stage impulsive control. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 40, 831–844 (2010)

    Article  Google Scholar 

  16. Zhang, H.G., Xie, Y.H., Wang, Z.L., Zheng, C.D.: Adaptive synchronization between two different chaotic neural networks with time delay. IEEE Trans. Neural Netw. 18, 1841–1845 (2007)

    Article  Google Scholar 

  17. Huang, H., Feng, G.: Synchronization of nonidentical chaotic neural networks with time delays. Neural Netw. 22, 869–874 (2009)

    Article  Google Scholar 

  18. Wang, Z.S., Zhang, H.G., Yu, W.: Robust stability of Cohen–Grossberg neural networks via state transmission matrix. IEEE Trans. Neural Netw. 20, 169–174 (2009)

    Article  Google Scholar 

  19. Zhang, D., Xu, J.C.: Projective synchronization of different chaotic time-delayed neural networks based on integral sliding mode controller. Appl. Math. Comput. 217, 164–174 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  20. Li, X.D., Fu, X.L.: Synchronization of chaotic delayed neural networks with impulsive and stochastic perturbations. Commun. Nonlinear Sci. Numer. Simul. 16, 885–894 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  21. Oliveira, J.J.: Global stability of a Cohen–Grossberg neural network with both time-varying and continuous distributed delays. Nonlinear Anal., Real World Appl. 12, 2861–2870 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  22. Wang, C.H., Kao, Y.G., Yang, G.W.: Exponential stability of impulsive stochastic fuzzy reaction-diffusion Cohen–Grossberg neural networks with mixed delays. Neurocomputing 89, 55–63 (2012)

    Article  Google Scholar 

  23. Wan, A., Qiao, H., Peng, J., Wang, M.: Delay-independent criteria for exponential stability of generalized Cohen–Grossberg neural networks with discrete delays. Phys. Lett. A 353, 151–157 (2006)

    Article  MATH  Google Scholar 

  24. Yu, J., Zhang, K., Fei, S.: Further results on mean square exponential stability of uncertain stochastic delayed neural networks. Commun. Nonlinear Sci. Numer. Simul. 14, 1582–1589 (2009)

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Yanchao Shi.

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Shi, Y., Zhu, P. Adaptive synchronization of different Cohen–Grossberg chaotic neural networks with unknown parameters and time-varying delays. Nonlinear Dyn 73, 1721–1728 (2013). https://doi.org/10.1007/s11071-013-0898-4

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  • DOI: https://doi.org/10.1007/s11071-013-0898-4

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