Fixed-time synchronization of delayed memristor-based recurrent neural networks

Research Paper


This paper focuses on the fixed-time synchronization control methodology for a class of delayed memristor-based recurrent neural networks. Based on Lyapunov functionals, analytical techniques, and together with novel control algorithms, sufficient conditions are established to achieve fixed-time synchronization of the master and slave memristive systems. Moreover, the settling time of fixed-time synchronization is estimated, which can be adjusted to desired values regardless of the initial conditions. Finally, the corresponding simulation results are included to show the effectiveness of the proposed methodology derived in this paper.


memristor fixed-time synchronization nonlinear control master-slave systems time delays 


  1. 1.
    Chua L O. Memristor-the missing circut element. IEEE Trans Circ Theory, 1971, 18: 507–519CrossRefGoogle Scholar
  2. 2.
    Chua L O, Kang S M. Memristive devices and systems. Proc IEEE, 1976, 64: 209–223MathSciNetCrossRefGoogle Scholar
  3. 3.
    Strukov D B, Snider G S, Stewart D R, et al. The missing memristor found. Nature, 2008, 453: 80–83CrossRefGoogle Scholar
  4. 4.
    Snider G S. Self-organized computation with unreliable, memristive nanodevices. Nanotechnology, 2007, 18: 365202CrossRefGoogle Scholar
  5. 5.
    Wen S P, Zeng Z G, Huang T W, et al. Fuzzy modeling and synchronization of different memristor-based chaotic circuits. Phys Lett A, 2013, 377: 2016–2021MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Landsman A S, Schwartz I B. Complete chaotic synchronization in mutually coupled time-delay systems. Phys Rev E Stat Nonlin Soft Matter Phys, 2007, 5: 26–33Google Scholar
  7. 7.
    Cui B T, Lou X Y. Synchronization of chaotic recurrent neural networks with time-varying delays using nonlinear feedback control. Chaos Solitons Fract, 2009, 39: 288–294CrossRefMATHGoogle Scholar
  8. 8.
    Gan Q T, Xu R, Kang X B. Synchronization of chaotic neural networks with mixed time delays. Commun Nonlinear Sci Numer Simul, 2011, 16: 966–974MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Molaei M R, Umut Ö. Generalized synchronization of nuclear spin generator system. Chaos Solitons Fract, 2008, 37: 227–232MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Cao J D, Rakkiyappan R, Maheswari K, et al. Exponential H filtering analysis for discrete-time switched neural networks with random delays using sojourn probabilities. Sci China Tech Sci, 2016, 59: 387–402CrossRefGoogle Scholar
  11. 11.
    Suddheerm K S, Sabir M. Adaptive function projective synchronization of two-cell Quantum-CNN chaotic oscillators with uncertain parameters. Phys Lett A, 2009, 373: 1847–1851CrossRefMATHGoogle Scholar
  12. 12.
    Chen S, Cao J D. Projective synchronization of neural networks with mixed time-varying delays and parameter mismatch. Nonlinear Dyn, 2012, 67: 1397–1406MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Cao J D, Li L L. Cluster synchronization in an array of hybrid coupled neural networks with delay. Neural Netw, 2009, 22: 335–342CrossRefMATHGoogle Scholar
  14. 14.
    Li X D, Bohner M. Exponential synchronization of chaotic neural networks with mixe ddelays and impulsive effects via output coupling with delay feedback. Math Comp Model, 2010, 52: 643–653CrossRefMATHGoogle Scholar
  15. 15.
    Cao J D, Sivasamy R, Rakkaiyappan R. Sampled-data H synchronization of chaotic Lur’e systems with time delay. Circ Syst Sign Process, 2016, 35: 811–835MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Yang S F, Guo Z Y, Wang J. Global synchronization of multiple recurrent neural networks with time delays via impulsive interactions. IEEE Trans Neural Netw Learn Syst, in press. doi: 10.1109/TNNLS.2016.2549703Google Scholar
  17. 17.
    Ding S B, Wang Z S. Stochastic exponential synchronization control of memristive neural networks with multiple time-varying delays. Neurocomputing, 2015, 162: 16–25CrossRefGoogle Scholar
  18. 18.
    Li R X, Wei H Z. Synchronization of delayed Markovian jump memristive neural networks with reaction-diffusion terms via sampled data control. Int J Mach Learn Cyber, 2016, 7: 157–169CrossRefGoogle Scholar
  19. 19.
    Abdurahman A, Jiang H J, Teng Z D. Finite-time synchronization for memristor-based neural networks with timevarying delays. Neural Netw, 2015, 69: 20–28CrossRefGoogle Scholar
  20. 20.
    Wang L M, Shen Y, Yin Q, et al. Adaptive synchronization of memristor-based neural networks with time-varying delays. IEEE Trans Neural Netw Learn Syst, 2015, 26: 2033–2042MathSciNetCrossRefGoogle Scholar
  21. 21.
    Chen J J, Zeng Z G, Jiang P. Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks. Neural Netw, 2014, 51: 1–8CrossRefMATHGoogle Scholar
  22. 22.
    Wen S P, Zeng Z G, Huang T W, et al. Exponential adaptive lag synchronization of memristive neural networks via fuzzy method and applications in pseudorandom number generators. IEEE Trans Fuzzy Syst, 2014, 22: 1704–1713CrossRefGoogle Scholar
  23. 23.
    Ding S B, Wang Z S. Lag quasi-synchronization for memristive neural networks with switching jumps mismatch. Neural Comput Appl, in press. doi: 10.1007/s00521-016-2291-yGoogle Scholar
  24. 24.
    Yang S F, Guo Z Y, Wang J. Robust synchronization of multiple memristive neural networks with uncertain parameters via nonlinear coupling. IEEE Trans Syst Man Cyber Syst, 2015, 45: 1077–1086CrossRefGoogle Scholar
  25. 25.
    Wan Y, Cao J D. Periodicity and synchronization of coupled memristive neural networks with supremums. Neurocomputing, 2015, 159: 137–143CrossRefGoogle Scholar
  26. 26.
    Polyakov A. Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans Autom Control, 2012, 57: 2106–2110MathSciNetCrossRefGoogle Scholar
  27. 27.
    Levant A. On fixed and finite time stability in sliding mode control. In: Proceedings of the 52nd IEEE Conference on Decision and Control, Florence, 2013. 4260–4265CrossRefGoogle Scholar
  28. 28.
    Parsegv S, Polyakov A, Shcherbakov P. Nonlinear fixed-time control protocol for uniform allocation of agents on a segment. In: Proceedings of the 51st IEEE Conference on Decision and Control, Maui, 2013. 7732–7737Google Scholar
  29. 29.
    Parsegv S, Polyakov A, Shcherbakov P. On fixed and finite time stability in sliding mode control. In: Proceedings of the 4th IFAC Workshop on Distributed Estimation and Control in Networked Systems, Koblenz, 2013. 110–115Google Scholar
  30. 30.
    Zhou Y J, Sun C Y. Fixed time synchronization of complex dynamical networks. In: Proceedings of the Chinese Intelligent Automation Conference. Berlin: Springer, 2015. 338: 163–170Google Scholar
  31. 31.
    Zuo Z. Non-singular fixed-time terminal sliding mode control of non-linear systems. IET Control Theory Appl, 2015, 9: 545–552MathSciNetCrossRefGoogle Scholar
  32. 32.
    Liu X W, Chen T P. Fixed-time cluster synchronization for complex networks via pinning control. arXiv:1509.03350Google Scholar
  33. 33.
    Wan Y, Cao J D, Wen G H, et al. Robust fixed-time synchronization of delayed Cohen-Grossberg neural networks. Neural Netw, 2016, 73: 86–94CrossRefGoogle Scholar
  34. 34.
    Clarke F. Optimization and Nonsmooth Analysis. Philadelphia: SIAM, 1987MATHGoogle Scholar
  35. 35.
    Hardy G, Littlewood J, Polya G. Inequalities. 2nd ed. Cambridge: Cambridge University Press, 1952MATHGoogle Scholar
  36. 36.
    Forti M, Grazzini M, Nistri P, et al. Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipschitz activations. Phys D Nonlin Phenom, 2006, 214: 88–99MathSciNetCrossRefMATHGoogle Scholar
  37. 37.
    Chua L O. Resistance switching memories are memristor. Appl Phys A, 2011, 102: 765–783CrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.School of Mathematics, and Research Center for Complex Systems and Network SciencesSoutheast UniversityNanjingChina

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