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Lag synchronization for fractional-order memristive neural networks via period intermittent control

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Abstract

In this paper, an intermittent control scheme is adopted to deal with the synchronization problem of fractional-order memristive neural networks(FMNNs) with switching jumps mismatch. Considering the inherent characteristic of FMNNs, a fractional-order differential inequality is introduced. Based on differential inclusions theory and the properties of Mittag Leffler function, some intermittent synchronization criteria are derived. The synchronization regain which is related to order \(\alpha \), control period T and the control width \(\delta \) is discussed in details. In addition, the lag complete synchronization criteria of FMNNs with switching jumps match are also obtained by period intermittent control. Finally, numerical simulations are presented to verify the effectiveness of the theoretical analysis.

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References

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

    Book  MATH  Google Scholar 

  2. Aubin, J.P., Frankowska, H.: Set-Valued Analysis. Springer, Berlin (2009)

    Book  MATH  Google Scholar 

  3. Bao, H.B., Park, J.H., Cao, J.D.: Adaptive synchronization of fractional-order memristor-based neural networks with time delay. Nonlinear Dyn. 82(3), 1343–1354 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bao, H.B., Park, J.H., Cao, J.D.: Exponential synchronization of coupled Stochastic Memristor-Based Neural Networks With Time-Varying Probabilistic Delay Coupling and Impulsive Delay. IEEE Trans. Neural Netw. Learn. Syst. 27(1), 190–201 (2016)

    Article  MathSciNet  Google Scholar 

  5. Bhrawy, A.H., Doha, E.H., Baleanu, D., Ezz-Eldien, S.S.: A spectral tau algorithm based on Jacobi operational matrix for numerical solution of time fractional diffusion-wave equations. J. Comput. Phys. 293, 142–156 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  6. Chen, W., Ye, L., Sun, H.: Fractional diffusion equations by the Kansa method. Comput. Math. Appl. 59(5), 1614–1620 (2010)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  8. Chua, L.: Resistance switching memories are memristors. Appl. Phys. A 102(4), 765–783 (2011)

    Article  MATH  Google Scholar 

  9. Diethelm, K.: The Analysis of Fractional Differential Equations. Springer, Berlin (2010)

    Book  MATH  Google Scholar 

  10. Ding, S.B., Wang, Z.S.: Lag quasi-synchronization for memristive neural networks with switching jumps mismatch. Neural Comput. Appl. 1–12 (2016). doi:10.1007/s00521-016-2291-y

  11. Duan, S., Hu, X., Dong, Z., et al.: Memristor-based cellular nonlinear/neural network: design, analysis, and applications. IEEE Trans. Neural Netw. Learn. Syst. 26(6), 1202–1213 (2015)

    Article  MathSciNet  Google Scholar 

  12. Duarte-Mermoud, M.A., Aguila-Camacho, N., Gallegos, J.A., Castro-Linares, R.: Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems. Commun. Nonlinear Sci. Numer. Simul. 22(1), 650–659 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  13. Feng, J., Yang, P., Zhao, Y.: Cluster synchronization for nonlinearly time-varying delayed coupling complex networks with stochastic perturbation via periodically intermittent pinning control. Appl. Math. Comput. 291, 52–68 (2016)

    MathSciNet  Google Scholar 

  14. Filippov, A.F.: Differential equations with discontinuous righthand sides. In: Arscott, F.M. (ed.) Mathematics and its Applications (Soviet Series). Kluwer Academic Publisher, Boston (1988)

  15. Forti, M., Nistri, P., Quincampoix, M.: Generalized neural network for nonsmooth nonlinear programming problems. IEEE Trans. Circuits Syst. I: Regul. Pap. 51(9), 1741–1754 (2004)

    Article  MathSciNet  Google Scholar 

  16. Forti, M., Nistri, P., Papini, D.: Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain. IEEE Trans. Neural Netw. 16(6), 1449–1463 (2005)

    Article  Google Scholar 

  17. Henderson, J., Ouahab, A.: Fractional functional differential inclusions with finite delay. Nonlinear Anal. Theory Methods Appl. 70(5), 2091–2105 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  18. Hu, J., Wang, J.: Global uniform asymptotic stability of memristor-based recurrent neural networks with time delays. IEEE International Joint Conference on Neural Networks, 1–8 (2010)

  19. Isfer, L.A.D., Lenzi, E.K., Teixeira, G.M., Lenzi, M.K.: Fractional control of an industrial furnace. Acta Sci. Technol. 32(3), 279–285 (2010)

    Google Scholar 

  20. Kilbas, A.A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006)

    MATH  Google Scholar 

  21. Li, N., Cao, J.D.: Lag synchronization of memristor-based coupled neural networks via \(\omega \)-measure. IEEE Trans. Neural Netw. Learn. Syst. 27(3), 686–697 (2016)

    Article  MathSciNet  Google Scholar 

  22. Machado, J.T., Kiryakova, V., Mainardi, F.: Recent history of fractional calculus. Commun. Nonlinear Sci. Numer. Simul. 16, 1140–1153 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  23. Oldham, K.B.: Fractional differential equations in electrochemistry. Adv. Eng. Softw. 41(1), 9–12 (2010)

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  25. Pldlubny, I.: Fractional Differential Equations. Academic Press, New York (1999)

    Google Scholar 

  26. Sharifi, M.J., Banadaki, Y.M.: 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)

    Article  Google Scholar 

  27. Shi, L., Yang, X., Li, Y., et al.: Finite-time synchronization of nonidentical chaotic systems with multiple time-varying delays and bounded perturbations. Nonlinear Dyn. 83(1–2), 75–87 (2016)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  29. Szabo, T.L., Wu, J.: A model for longitudinal and shear wave propagation in viscoelastic media. J. Acoust. Soc. Am. 107(5), 2437–2446 (2000)

    Article  Google Scholar 

  30. Toledo, H.R., Rico, R.V., Iglesias, S.G.A., Diwekar, U.M.: A fractional calculus approach to the dynamic optimization of biological reactive systems. Part I: fractional models for biological reactions. Chem. Eng. Sci. 117, 217–228 (2014)

    Article  Google Scholar 

  31. Tour, J.M., He, T.: Electronics: the fourth element. Nature 453, 42–43 (2008)

    Article  Google Scholar 

  32. Velmurugan, G., Rakkiyappan, R.: Hybrid projective synchronization of fractional-order memristor-based neural networks with time delays. Nonlinear Dyn. 83(1–2), 419–432 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  33. Wang, L.M., Shen, Y., Yin, Q., Zhang, G.D.: Adaptive synchronization of memristor-based neural networks with time-varying delays. IEEE Trans. Neural Netw. Learn. Syst. 26(9), 2033–2042 (2015)

    Article  MathSciNet  Google Scholar 

  34. Wang, L., Shen, Y., Yin, Q., Zhang, G.: Adaptive synchronization of memristor-based neural networks with time-varying delays. IEEE Trans. Neural Netw. Learn. Syst. 26, 2033–2042 (2015)

    Article  MathSciNet  Google Scholar 

  35. Wen, S., Zeng, Z., Huang, T., Zhang, Y.: Exponential adaptive lag synchronization of memristive neural networks via fuzzy method and applications in pseudorandom number generators. IEEE Trans. Fuzzy Syst. 22(6), 1704–1713 (2014)

    Article  Google Scholar 

  36. Wen, S., Zeng, Z., Huang, T., et al.: Lag synchronization of switched neural networks via neural activation function and applications in image encryption. IEEE Trans. Neural Netw. Learn. Syst. 26(7), 1493–1502 (2015)

    Article  MathSciNet  Google Scholar 

  37. Wen, S., Zeng, Z., Chen, M.Z., et al.: Synchronization of switched neural networks with communication delays via the event-triggered control. IEEE Trans. Neural Netw. Learn. Syst. 99, 1–10 (2016)

    Article  Google Scholar 

  38. Wen, G., Hu, G., Hu, J., et al.: Frequency regulation of source-grid-load systems: a compound control strategy. IEEE Trans. Ind. Inform. 12(1), 69–78 (2016)

    MathSciNet  Google Scholar 

  39. Wen, S., Huang, T., Yu, X., Chen, M.Z., Zeng, Z.: Sliding-mode control of memristive Chua’s systems via the event-based method. IEEE Trans. Circuits Syst. II: Express Briefs 64(1), 81–85 (2017)

    Article  Google Scholar 

  40. Wong, R., Zhao, Y.Q.: Exponential asymptotics of the Mittag-Leffler function. Constr. Approxi. 18(3), 355–385 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  41. Wu, A., Zeng, Z.: Anti-synchronization control of a class of memristive recurrent neural networks. Commun. Nonlinear Sci. Numer. Simul. 18(2), 373–385 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  42. Yu, J., Hu, C., Jiang, H., Fan, X.: Projective synchronization for fractional neural networks. Neural Netw. 49, 87–95 (2014)

    Article  MATH  Google Scholar 

  43. Zhang, S., Yu, Y., Wang, Q.: Stability analysis of fractional-order Hopfield neural networks with discontinuous activation functions. Neurocomputing 171, 1075–1084 (2016)

    Article  Google Scholar 

  44. Zhang, G., Shen, Y.: Exponential stabilization of memristor-based chaotic neural networks with time-varying delays via intermittent control. IEEE Trans. Neural Netw. Learn. Syst. 26(7), 1431–1441 (2015)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Science, Institute of Automation, Jiangnan University, Wuxi, 214122, People’s Republic of China

    Lingzhong Zhang, Yongqing Yang & Fei wang

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  1. Lingzhong Zhang
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  2. Yongqing Yang
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  3. Fei wang
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Corresponding author

Correspondence to Yongqing Yang.

Additional information

This work was jointly supported by the Natural Science Foundation of Jiangsu Province of China under Grant No. BK20161126, the Graduate Innovation Project of Jiangsu Province under Grant No. KYLX16_0778 and the Fundamental Research Funds for the Central Universities JUSRP51317B.

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Zhang, L., Yang, Y. & wang, F. Lag synchronization for fractional-order memristive neural networks via period intermittent control. Nonlinear Dyn 89, 367–381 (2017). https://doi.org/10.1007/s11071-017-3459-4

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  • DOI: https://doi.org/10.1007/s11071-017-3459-4

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