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Adaptive synchronization of chaotic Cohen–Crossberg neural networks with mixed time delays

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Abstract

In this paper, the problem of adaptive synchronization is investigated for a class of Cohen–Crossberg neural networks with mixed time delays. Based on a Lyapunov–Krasovskii functional and the invariant principle of function differential equations as well as the adaptive control and linear feedback with update law, a linear matrix inequality approach is developed to derive some novel sufficient conditions achieving synchronization of the two coupled networks with mixed time delays. In particular, the mixed time delays in this paper synchronously consist of constant delays, time-varying delays, and distributed delays, which are more general than those discussed in the previous literature. Therefore, the results obtained in this paper comprise and generalize those given in the previous literature. A numerical example and its simulation are provided to show the effectiveness of the theoretical results.

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References

  1. Agiza, H.N., Yassen, M.T.: Synchronization of Rossler and Chen chaotic dynamical systems using active control. Phys. Lett. A 278(4), 191–197 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  2. Boyd, S., Ghaoui, L., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia (1994)

    MATH  Google Scholar 

  3. Cao, J., Lu, J.: Adaptive synchronization of neural networks with or without time-varying delays. Chaos 16(1), 013133 (2006)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  5. Chen, G., Zhou, J., Liu, Z.: Global synchronization of coupled delayed neural networks and application to chaotic CNN models. Int. J. Bifurc. Chaos 14(7), 2229–2240 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  6. Cheng, C., Liao, T., Hwang, C.: Exponential synchronization of a class of chaotic neural networks. Chaos Solitons Fractals 24(1), 197–206 (2005)

    MATH  MathSciNet  Google Scholar 

  7. Cheng, C., Liao, T., Yan, J., Hwang, C.: Exponential synchronization of a class of neural networks with time-varying delays. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 36(1), 209–215 (2006)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  9. Cichocki, A., Unbehauen, R.: Neural Networks for Optimalition and Signal Processing. Wiley, New York (1993)

    Google Scholar 

  10. Cui, B., Lou, X.: Synchronization of chaotic recurrent neural networks with time-varying delays using nonlinear feedback control. Chaos Solitons Fractals 39(1), 288–294 (2009)

    Article  Google Scholar 

  11. Fotsin, H.B., Daafouz, J.: Adaptive synchronization of uncertain chaotic colpitts oscillators based on parameter identification. Phys. Lett. A 339(3–5), 304–315 (2005)

    Article  MATH  Google Scholar 

  12. Fotsin, H.B., Woafo, P.: Adaptive synchronization of a modified and uncertain chaotic Van der Pol–Duffing oscillator based on parameter identification. Chaos Solitons Fractals 24(5), 1363–1371 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  13. Gu, K.: An integral inequality in the stability problem of time-delay systems. In: Proceedings of 39th IEEE Conference on Decision and Control, Sydney, Australia, pp. 2805–2810 (2000)

  14. 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  Google Scholar 

  15. He, G., Cao, Z., Zhu, P., Ogura, H.: Controlling chaos in a chaotic neural network. Neural Netw. 16(8), 1195–1200 (2003)

    Article  Google Scholar 

  16. Heagy, J.F., Carroll, T.L., Pecora, L.M.: Experimental and numerical evidence for riddled basins in coupled chaotic systems. Phys. Rev. Lett. 73, 3528–3531 (1994)

    Article  Google Scholar 

  17. Huang, D.: Simple adaptive-feedback controller for identical chaos synchronization. Phys. Rev. E 71, 037203 (2005)

    Article  Google Scholar 

  18. Huang, L., Feng, R., Wang, M.: Synchronization of chaotic systems via nonlinear control. Phys. Lett. A 320(4), 271–275 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  19. Joya, G., Atencia, M.A., Sandoval, F.: Hopfield neural networks for optimization: study of the different dynamics. Neurocomputing 43(1–4), 219–237 (2002)

    Article  MATH  Google Scholar 

  20. Kakmeni, F., Bowong, S., Tchawoua, C.: Nonlinear adaptive synchronization of a class of chaotic systems. Phys. Lett. A 355, 47–54 (2006)

    Article  Google Scholar 

  21. Lei, Y., Xu, W., Zheng, H.: Synchronization of two chaotic nonlinear gyros using active control. Phys. Lett. A 343(1–3), 153–158 (2005)

    Article  MATH  Google Scholar 

  22. Li, W.J., Lee, T.: Hopfield neural networks for affine invariant matching. IEEE Trans. Neural Netw. 12(6), 1400–1410 (2001)

    Article  Google Scholar 

  23. Li, C., Liao, X., Zhang, X.: Impulsive stabilization and synchronization of a class of chaotic delay systems. Chaos 15, 023104 (2005)

    Article  MathSciNet  Google Scholar 

  24. Lu, J., Cao, J.: Adaptive complete synchronization of two identical or different chaotic (hyperchaotic) systems with fully unknown parameters. Chaos 15, 043901 (2005)

    Article  MathSciNet  Google Scholar 

  25. Mackevicius, V.: A note on synchronization of diffusion. Math. Comput. Simul. 52, 491–495 (2000)

    Article  MathSciNet  Google Scholar 

  26. Mahboobi, S.H., Shahrokhi, M., Pishkenari, H.N.: Observer-based control design for three well-known chaotic systems. Chaos Solitons Fractals 29(2), 381–392 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  27. Park, J.H.: Synchronization of Genesio chaotic system via backstepping approach. Chaos Solitons Fractals 27(5), 1369–1375 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  28. Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64(8), 821–824 (1990)

    Article  MathSciNet  Google Scholar 

  29. Salarieh, H., Alasty, A.: Adaptive synchronization of two chaotic systems with stochastic unknown parameters. Commun. Nonlinear Sci. Numer. Simul. 14(2), 508–519 (2009)

    Article  MathSciNet  Google Scholar 

  30. Sun, Y., Cao, J., Wang, Z.: Exponential synchronization of stochastic perturbed chaotic delayed neural networks. Neurocomputing 70, 2477–2485 (2007)

    Article  Google Scholar 

  31. Wang, C., Su, J.: A new adaptive variable structure control for chaotic synchronization and secure communication. Chaos Solitons Fractals 20(5), 967–977 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  32. Wang, K., Teng, Z., Jiang, H.: Adaptive synchronization of neural networks with time-varying delay and distributed delay. Physica A 387(2–3), 631–642 (2008)

    Article  Google Scholar 

  33. Young, S., Scott, P., Nasrabadi, N.: Object recognition using multilayer Hopfield neural network. IEEE Trans. Image Process. 6(3), 357–372 (1997)

    Article  Google Scholar 

  34. Yu, W., Cao, J.: Adaptive synchronization and lag synchronization of uncertain dynamical system with time delay based on parameter identification. Phys. Lett. A 375(2), 467–482 (2007)

    Google Scholar 

  35. Zhou, J., Chen, T., Xiang, L.: Robust synchronization of delayed neural networks based on adaptive control and parameters identification. Chaos Solitons Fractals 27(4), 905–913 (2006)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Ningbo University, Ningbo, 315211, Zhejiang, China

    Quanxin Zhu

  2. Department of Mathematics, Southeast University, Nanjing, 210096, Jiangsu, China

    Jinde Cao

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  1. Quanxin Zhu
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  2. Jinde Cao
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Correspondence to Quanxin Zhu.

Additional information

This work was jointly supported by the National Natural Science Foundation of China (10801056, 60874088), the Natural Science Foundation of Ningbo (201001A6011005), the Scientific Research Fund of Zhejiang Provincial Education Department, K.C. Wong Magna Fund in Ningbo University, and the Specialized Research Fund for the Doctoral Program of Higher Education (20070286003).

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Zhu, Q., Cao, J. Adaptive synchronization of chaotic Cohen–Crossberg neural networks with mixed time delays. Nonlinear Dyn 61, 517–534 (2010). https://doi.org/10.1007/s11071-010-9668-8

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