Exponential Lag Synchronization for Delayed Cohen-Grossberg Neural Networks with Discontinuous Activations

  • Abdujelil Abdurahman
  • Cheng Hu
  • Haijun Jiang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9377)


In this paper, we investigate the exponential lag synchronization of delayed Cohen-Grossberg neural networks with discontinuous activation functions. By employing the analysis technique and theory of the differential equations with discontinuous right-hand side, some novel lag synchronization criteria have been obtained. Finally, an example is given to illustrate the effectiveness of the obtained results.


Cohen-Grossberg neural network Exponential lag synchronization Discontinuous Time-delay 


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  1. 1.
    Guo, Z., Huang, L.: LMI conditions for global robust stability of delayed neural networks with discontinuous neuron activations. Appl. Math. Comput. 215, 889–900 (2009)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Liu, J., Liu, X., Xie, W.: Global convergence of neural networks with mixed time-varying delays and discontinuous neuron activations. Inf. Sci. 183, 92–105 (2012)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Lu, W., Chen, T.: Almost periodic dynamics of a class of delayed neural networks with discontinuous activations. Neural Comput. 20, 1065–1090 (2008)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems, Phys. Rev. Lett. 64, 821–824 (1990)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Yang, T., Chua, L.O.: Impulsive stabilization for control and synchronization of chaotic system: Theory and application to secure communication. IEEE Trans. Circuits Syst. I 44, 976–988 (1997)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Yao, C., Zhao, Q., Yu, J.: Complete synchronization induced by disorder in coupled chaotic lattices. Phys. Lett. A 377, 370–377 (2013)CrossRefGoogle Scholar
  7. 7.
    Liu, Q., Zhang, S.: Adaptive lag synchronization of chaotic Cohen-Grossberg neural networks with discrete delays. Chaos 22, 033123 (2012)Google Scholar
  8. 8.
    Yang, T., Chua, L.O.: Impulsive control and synchronization of nonlinear dynamical systems and application to secure communication. Int. J. Bifurcat. Chaos 7, 645–664 (1997)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Rosenblum, M.G., Pikovsky, A.S., Kurths, J.: From phase to lag synchronization in coupled chaotic oscillators. Phys. Rev. Lett. 78, 4193 (1997)CrossRefGoogle Scholar
  10. 10.
    Mainieri, R., Rehacek, J.: Projective synchronization in three-dimensional chaotic systems. Phys. Rev. Lett. 82, 304 (1999)CrossRefGoogle Scholar
  11. 11.
    Abdurahman, A., Jiang, H., Teng, Z.: Function projective synchronization of impulsive neural networks with mixed time-varying delays. Nonlinear Dyn. 78, 2627–2638 (2014)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Hu, C., Yu, J., Jiang, H., Teng, Z.: Exponential lag synchronization for neural networks with mixed delays via periodically intermittent control. Chaos 20, 023108 (2010)Google Scholar
  13. 13.
    Shahverdiev, E.M., Sivaprakasam, S., Shore, K.A.: Lag synchronization in time-delayed systems. Phys. Lett. A 292, 320–324 (2002)CrossRefGoogle Scholar
  14. 14.
    Sun, Y., Cao, J.: Adaptive lag synchronization of unknown chaotic delayed neural networks with noise perturbation. Phy. Lett. A 364, 277–285 (2007)CrossRefGoogle Scholar
  15. 15.
    Liu, X., Chen, T., Cao, J., Lu, W.: Dissipativity and quasi-synchronization for neural networks with discontinuous activations and parameter mismatches. Neural Networks 24, 1013–1021 (2011)CrossRefGoogle Scholar

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© Springer International Publishing Switzerland 2015

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Authors and Affiliations

  • Abdujelil Abdurahman
    • 1
  • Cheng Hu
    • 1
  • Haijun Jiang
    • 1
  1. 1.College of Mathematics and System SciencesXinjiang UniversityUrumqiP.R. China

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