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New results on synchronization control of delayed memristive neural networks

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Abstract

This paper is focused on the exponential synchronization for a class of delayed memristive neural networks. Basing on nonsmooth analysis and control theory, several new sufficient conditions concerning global exponential synchronization are obtained for the proposed system. In addition, the obtained results complement and extend earlier publications on memristive or conventional neural network dynamical systems with continuous or discontinuous right-hand side. Finally, numerical simulations illustrate the effectiveness of our results.

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References

  1. Chua, L.O.: Memristor—the missing circuit element. IEEE Trans. Circuit Theory CT 18, 507–519 (1971)

    Article  Google Scholar 

  2. Strukov, D.B., Snider, G.S., Stewart, G.R., Williams, R.S.: The missing memristor found. Nature 453, 80–83 (2008)

    Article  Google Scholar 

  3. Chua, L.O.: Resistence switching memories are memristor. Appl. Phys. A 102, 765–783 (2011)

    Article  Google Scholar 

  4. Sharifiy, M.J., Banadaki, Y.M.: General spice models for memristor and application to circuit simulation of memristor-based synapses and memory cells. J. Circuit. Syst. Comp. 19, 407–424 (2010)

    Article  Google Scholar 

  5. Pershin, Y.V., Di Ventra, M.: Experimental demonstration of associative memory with memristive neural networks. Neural Netw. 23, 881–886 (2010)

    Article  Google Scholar 

  6. Itoh, M., Chua, L.O.: Memristor cellular automata and memristor discrete-time cellular neural networks. Int. J. Bifur. Chaos 19, 3605–3656 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Zhang, G.D., Shen, Y., Sun, J.: Global exponential stability of a class of memristor-based recurrent neural networks with time-varying delays. Neurocomputing 97, 149–154 (2012)

    Article  Google Scholar 

  8. Wu, A.L., Zeng, Z.G.: New global exponential stability results for a memristive neural system with time-varying delays. Neurocomputing 144, 553–559 (2014)

    Article  Google Scholar 

  9. Wu, A.L., Zeng, Z.G.: Exponential stabilization of memristive neural networks with time delays. IEEE Trans. Neural Netw. Learn. Syst. 23, 1919–1929 (2012)

    Article  Google Scholar 

  10. Wen, S., Zeng, Z., Huang, T., Chen, Y.: Passivity analysis of memristor-based recurrent neural networks with time-varying delays. J. Franklin Inst. 350, 2354–2370 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  11. Duan, L., Huang, L.H.: Periodicity and dissipativity for memristor-based mixed time-varying delayed neural networks via differential inclusions. Neural Netw. 57, 12–22 (2014)

    Article  Google Scholar 

  12. Zhang, G.D., Shen, Y., Yin, Q., Sun, J.W.: Global exponential periodicity and stability of a class of memristor-based recurrent neural networks with multiple delays. Inf. Sci. 232, 386–396 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  13. Chen, J.J., Zeng, Z.G., Jiang, P.: On the periodic dynamics of memristor-based neural networks with time-varying delays. Inf. Sci. 279, 358–373 (2014)

    Article  MathSciNet  Google Scholar 

  14. Wu, A.L., Wen, S.P., Zeng, Z.G.: Synchronization control of a class of memristor-based recurrent neural networks. Inf. Sci. 183, 106–116 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  15. Yang, X., Cao, J., Yu, W.: Exponential synchronization of memristive Cohen–Grossberg neural networks with mixed delays. Cogn. Neurodyn. 8, 239–249 (2014)

    Article  Google Scholar 

  16. Zhang, G.D., Shen, Y.: Exponential synchronization of delayed memristor-based chaotic neural networks via periodically intermittent control. Neural Netw. 55, 1–10 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  17. Wu, A.L., Zeng, Z.G.: Lagrange stability of neural networks with memristive synapses and multiple delays. Inf. Sci. 280, 135–151 (2014)

    Article  MathSciNet  Google Scholar 

  18. Guo, Z.Y., Wang, J., Yan, Z.: Global exponential dissipativity and stabilization of memristor-based recurrent neural networks with time-varying delays. Neural Netw. 48, 158–172 (2013)

    Article  MATH  Google Scholar 

  19. Guo, Z.Y., Wang, J., Yan, Z.: Attractivity analysis of memristor-based cellular neural networks with time-varying delays. IEEE Trans. Neural Netw. Learn. Syst. 25, 704–717 (2014)

    Article  Google Scholar 

  20. Li, N., Yuan, H.Q., Sun, H.Y., Zhang, Q.L.: An impulsive multi-delayed feedback control method for stabilizing discrete chaotic systems. Nonlinear Dyn. 73, 1187–1199 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  21. Duan, L., Huang, L.H.: Existence and stability of periodic solution for mixed time-varying delayed neural networks with discontinuous activations. Neurocomputing 123, 255–265 (2014)

    Article  Google Scholar 

  22. Duan, L., Huang, L.H., Guo, Z.Y.: Stability and almost periodicity for delayed high-order Hopfield neural networks with discontinuous activations. Nonlinear Dyn. 77, 1469–1484 (2014)

    Article  MathSciNet  Google Scholar 

  23. Wang, J.L., Wu, H.N.: Synchronization criteria for impulsive complex dynamical networks with time-varying delay. Nonlinear Dyn. 70, 13–24 (2012)

    Article  MATH  Google Scholar 

  24. Zhang, G.D., Shen, Y., Chen, B.S.: Hopf bifurcation of a predator–prey system with predator harvesting and two delays. Nonlinear Dyn. 73, 2119–2131 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  25. Yang, X., Cao, J., Long, Y., Rui, W.G.: Adaptive lag synchronization for competitive neural networks with mixed delays and uncertain hybrid perturbations. IEEE Trans. Neural Netw. 21, 1656–1667 (2010)

    Article  Google Scholar 

  26. Xu, S.Y., Chu, Y.M., Lu, J.W.: New results on global exponential stability of recurrent neural networks with time-varying delays. Phys. Lett. A 352, 371–379 (2006)

    Article  MATH  Google Scholar 

  27. Wu, H.Q.: Global stability analysis of a general class of discontinuous neural networks with linear growth activation functions. Inf. Sci. 179, 3432–3441 (2009)

    Article  MATH  Google Scholar 

  28. Huang, T.W., Li, C.D., Yu, W., Chen, G.: Synchronization of delayed chaotic systems with parameter mismatches by using intermittent linear state feedback. Nonlinearity 22, 569–584 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  29. Sun, W.G., Li, S.X.: Generalized outer synchronization between two uncertain dynamical networks. Nonlinear Dyn. 77, 481–489 (2014)

    Article  Google Scholar 

  30. Martinez-Guerra, R., Mata-Machuca, J.L.: Fractional generalized synchronization in a class of nonlinear fractional order systems. Nonlinear Dyn. 77, 1237–1244 (2014)

    Article  MathSciNet  Google Scholar 

  31. Cai, S.M., Liu, Z., Xu, F., Shen, J.: Periodically intermittent controlling complex dynamical networks with time-varying delays to a desired orbit. Phys. Lett. A 373, 3846–3854 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  32. Cai, S.M., Zhou, P.P., Liu, Z.R.: Pinning synchronization of hybrid-coupled directed delayed dynamical network via intermittent control. Chaos 24, 033102 (2014)

    Article  Google Scholar 

  33. Cai, S.M., Zhou, P.P., Liu, Z.R.: Synchronization analysis of directed complex networks with time-delayed dynamical nodes and impulsive effects. Nonlinear Dyn. 76, 1677–1691 (2014)

    Article  MathSciNet  Google Scholar 

  34. Forti, M., Nistri, P., Papini, D.: Global exponential stability and global convergence infinite time of delayed neural networks with infinite gain. IEEE Trans. Neural Netw. 16, 1449–1463 (2005)

    Article  Google Scholar 

  35. Filippov, A.F.: Differential Equations with Discontinuous Right-hand Sides. Kluwer, Dordrecht (1988)

    Book  MATH  Google Scholar 

  36. Aubin, J.P., Cellina, A.: Differential Inclusions. Springer, Berlin (1984)

    Book  MATH  Google Scholar 

  37. Clarke, F.H., Ledyaev, Y.S., Stem, R.J., Wolenski, R.R.: Nonsmooth Analysis and Control Theory. Springer, New York (1998)

    MATH  Google Scholar 

Download references

Acknowledgments

The authors gratefully acknowledge anonymous referees’ comments and patient work. This work is supported by the National Science Foundation of China under Grant Nos. 11271146 and 61374085. The Fundamental Research Funds for the Central Universities of South-Central University For Nationalities (CZQ15019) and the Key Program of National Natural Science Foundation of China under Grant No. 61134012.

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Authors and Affiliations

  1. School of Mathematics and Statistics, South-Central University for Nationalities, Wuhan, 430074, China

    Guodong Zhang & Junhao Hu

  2. School of Automation, Huazhong University of Science and Technology, Wuhan, 430074, China

    Yi Shen

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  1. Guodong Zhang
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  2. Junhao Hu
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  3. Yi Shen
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Correspondence to Guodong Zhang.

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Zhang, G., Hu, J. & Shen, Y. New results on synchronization control of delayed memristive neural networks. Nonlinear Dyn 81, 1167–1178 (2015). https://doi.org/10.1007/s11071-015-2058-5

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  • DOI: https://doi.org/10.1007/s11071-015-2058-5

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