Global Exponential Anti-synchronization of Coupled Memristive Chaotic Neural Networks with Time-Varying Delays

  • Zheng Yan
  • Shuzhan Bi
  • Xijun Xue
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9377)


This paper investigates the problem of global exponential anti-synchronization of a class of memristive chaotic neural networks with time-varying delays. First, a memrsitive neural network is modeled. Then, considering the state-dependent properties of the memristor, a new fuzzy model employing parallel distributed compensation (PDC) provides a new way to analyze the complicated memristive neural networks with only two subsystems. And the controller is dependent on the output of the system in the case of packed circuits. An illustrative example is also presented to show the effectiveness of the results.


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  1. 1.
    Jo, S., Chang, T., Ebong, I., Bhadviya, B., Mazumder, P., Lu, W.: Nanoscale memristor device as synapse in neuromorphic systems. Nanotech. Lett. 10, 1297–1301 (2010)Google Scholar
  2. 2.
    Ananthanarayanan, R., Eser, S., Simon, H., Modha, D.: Proceedings of 2009 IEEE/ACM Conference High Performance Networking Computing, Portland, OR, November 2009Google Scholar
  3. 3.
    Smith, L.: Handbook of Nature-Inspired and Innovative Computing: Integrating Classical Models with Emerging Technologies, pp. 433–475. Springer, New YorkGoogle Scholar
  4. 4.
    Strukov, D., Snider, G., Stewart, D., Williams, R.: The missing memristor found. Nature 453, 80–83 (2008)CrossRefGoogle Scholar
  5. 5.
    Chua, L.: Memristor-The missing circuit element. IEEE Trans. Circuits Theory 18, 507–519 (1971)CrossRefGoogle Scholar
  6. 6.
    Sharifiy, M., Banadaki, Y.: General spice models for memristor and application to circuit simulation of memristor-based synapses and memory cells. J. Circuits Syst. Comput. 19, 407–424 (2010)CrossRefGoogle Scholar
  7. 7.
    Choi, T., Shi, B., Boahen, K.: An on-off orientation selective address event representation image transceiver chip. IEEE Trans. Circuits Syst. I 51, 342–353 (2004)CrossRefGoogle Scholar
  8. 8.
    Indiveri, G.: A neuromorphic VLSI device for implementing 2-D selective attention systems. IEEE Trans. Neural Networks 12, 1455–1463 (2001)CrossRefGoogle Scholar
  9. 9.
    Liu, S., Douglas, R.: Temporal coding in a silicon network of integrate-and-fire neurons. IEEE Trans. Neural Networks 15, 1305–1314 (2004)CrossRefGoogle Scholar
  10. 10.
    Li, C., Feng, G.: Delay-interval-dependent stability of recurrent neural networks with time-varying delay. Neurocomput. 72, 1179–1183 (2009)CrossRefGoogle Scholar
  11. 11.
    Li, C., Feng, G., Liao, X.: Stabilization of nonlinear system via periodically intermittent control. IEEE Trans. Circuit Syst. II 54, 1019–1023 (2007)CrossRefGoogle Scholar
  12. 12.
    Shen, Y., Wang, J.: An improved algebraic criterion for global exponential stability of recurrent neural networks with time-varying delays. IEEE Trans. Neural Networks 19, 528–531 (2008)CrossRefGoogle Scholar
  13. 13.
    Song, Q.: Synchronization analysis in an array of asymmetric neural networks with time-varying delays and nonlinear coupling. Appl. Math. Comput. 216, 1605–1613 (2010)MathSciNetzbMATHGoogle Scholar
  14. 14.
    Song, Q., Zhao, Z., Yang, J.: Passivity and passification for stochastic Takagi-Sugeno fuzzy systems with mixed time-varying delays. Neurocomput (2013). doi:10.1016/j.neurocom.2013.06.018Google Scholar
  15. 15.
    Cao, J., Chen, G., Li, P.: Global synchronization in an array of delayed neural networks with hybrid coupling. IEEE Trans. Syst. Man Cybern. B 38, 488–498 (2008)CrossRefGoogle Scholar
  16. 16.
    Juang, C., Chen, T., Cheng, W.: Speedup of implementing fuzzy neural networks with high-dimensional inputs through parallel processing on graphic processing units. IEEE Trans. Fuzzy Syst. 19, 717–728 (2011)CrossRefGoogle Scholar
  17. 17.
    Li, J., Kazemian, H., Afzal, M.: Neural network approaches for noisy language modeling. IEEE Trans. Neural Networks Learn. Syst. (2013). doi:10.1109/TNNLS.2013.2263557Google Scholar
  18. 18.
    Park, M., Kwon, O., Park, J., Lee, S., Cha, E.: Synchronization criteria for coupled neural networks with interval time-varying delays and leakage delay. Appl. Math. Comput. 218, 6762–6775 (2012)MathSciNetzbMATHGoogle Scholar
  19. 19.
    Zhang, H., Ma, T., Huang, G., Wang, Z.: Robust global exponential synchronization of uncertain chaotic delayed neural networks via dualstage impulsive control. IEEE Trans. Syst. Man Cybern. B Cybern. 40, 831–844 (2010)CrossRefGoogle Scholar
  20. 20.
    Dong, J., Wang, Y., Yang, G.: Control synthesis of continuous-time T-S fuzzy systems with local nonlinear models. IEEE Trans. Syst. Man Cybern. B Cybern. 39, 1245–1258 (2009)CrossRefGoogle Scholar
  21. 21.
    Liu, X., Zhong, S.: T-S fuzzy model-based impulsive control of chaotic systems with exponential decay rate. Phys. Lett. A 370, 260–264 (2007)CrossRefGoogle Scholar
  22. 22.
    Park, C., Cho, Y.: T-S model based indirect adaptive fuzzy control using online parameter estimation. IEEE Trans. Syst. Man Cybern. B Cybern. 34, 2293–2302 (2004)CrossRefGoogle Scholar
  23. 23.
    Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modelling and control. IEEE Trans. Syst. Man Cybern. SMC-15, 116–132 (1985)Google Scholar
  24. 24.
    Zhao, W., Tan, Y.: Harmless delay for global exponential stability of Cohen-Grossberg neural networks. Math. Comput. Simul. 74, 47–57 (2007)MathSciNetCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Shannon LabHuawei Technologies Co., Ltd.BeijingChina

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