Science China Technological Sciences

, Volume 61, Issue 4, pp 612–622 | Cite as

Synchronization criteria for multiple memristor-based neural networks with time delay and inertial term

  • Ning Li
  • JinDe Cao


This present work uses different methods to synchronize the inertial memristor systems with linear coupling. Firstly, the math- ematical model of inertial memristor-based neural networks (IMNNs) with time delay is proposed, where the coupling matrix satisfies the diffusion condition, which can be symmetric or asymmetric. Secondly, by using differential inclusion method and Halanay inequality, some algebraic self-synchronization criteria are obtained. Then, via constructing effective Lyapunov functional, designing discontinuous control algorithms, some new sufficient conditions are gained to achieve synchronization of networks. Finally, two illustrative simulations are provided to show the validity of the obtained results, which cannot be contained by each other.


memristor-based neural networks (MNNs) inertial term synchronization discontinuous control 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Chua L. Memristor The missing circuit element. IEEE Trans Circuit Theor, 1971, 18: 507–C519CrossRefGoogle Scholar
  2. 2.
    Strukov D B, Snider G S, Stewart D R, et al. The missing memristor found. Nature, 2008, 453: 80–C83CrossRefGoogle Scholar
  3. 3.
    Tour J M, He T. Electronics: The fourth element. Nature, 2008, 453: 42–C43CrossRefGoogle Scholar
  4. 4.
    Wang W, Li L, Peng H, et al. Anti-synchronization of coupled memris- tive neutral-type neural networks with mixed time-varying delays via randomly occurring control. Nonlinear Dyn, 2016, 83: 2143–C2155CrossRefzbMATHGoogle Scholar
  5. 5.
    Thomas A. Memristor-based neural networks. J Phys D-Appl Phys, 2013, 46: 093001CrossRefGoogle Scholar
  6. 6.
    Wen S, Zeng Z, Huang T. Exponential stability analysis of memristor- based recurrent neural networks with time-varying delays. Neurocom- puting, 2012, 97: 233–C240CrossRefGoogle Scholar
  7. 7.
    Chen J, Zeng Z, Jiang P. Global Mittag-Leffler stability and synchro- nization of memristor-based fractional-order neural networks. Neural Networks, 2014, 51: 1–C8CrossRefzbMATHGoogle Scholar
  8. 8.
    Guo Z, Wang J, Yan Z. Global exponential dissipativity and stabiliza- tion of memristor-based recurrent neural networks with time-varying delays. Neural Networks, 2013, 48: 158–C172CrossRefzbMATHGoogle Scholar
  9. 9.
    Guo Z, Wang J, Yan Z. Attractivity analysis of memristor-based cellu- lar neural networks with time-varying delays. IEEE Trans Neural Netw Learn Syst, 2014, 25: 704–C717CrossRefGoogle Scholar
  10. 10.
    Bao H B, Cao J D. Projective synchronization of fractional-order memristor-based neural networks. Neural Networks, 2015, 63: 1–C9CrossRefzbMATHGoogle Scholar
  11. 11.
    Yu J, Hu C, Jiang H, et al. Projective synchronization for fractional neural networks. Neural Networks, 2014, 49: 87–C95CrossRefzbMATHGoogle Scholar
  12. 12.
    Zhang W, Li C, Huang T, et al. Synchronization of memristor-based coupling recurrent neural networks with time-varying delays and im-pulses. IEEE Trans Neural Netw Learn Syst, 2015, 26: 3308–C3313MathSciNetCrossRefGoogle Scholar
  13. 13.
    Li N, Cao J. New synchronization criteria for memristor-based net- works: Adaptive control and feedback control schemes. Neural Net-works, 2015, 61: 1–C9CrossRefzbMATHGoogle Scholar
  14. 14.
    Wu A, Wen S, Zeng Z. Synchronization control of a class of memristor- based recurrent neural networks. Inf Sci, 2012, 183: 106–C116MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Pecora L M, Carroll T L. Synchronization in chaotic systems. Phys Rev Lett, 1990, 64: 821–C824MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Abdurahman A, Jiang H, Teng Z. Finite-time synchronization for memristor-based neural networks with time-varying delays. Neural Networks, 2015, 69: 20–C28CrossRefGoogle Scholar
  17. 17.
    Liu X, Ho D W C, Cao J, et al. Discontinuous observers design for finite-time consensus of multiagent systems with external disturbances. IEEE Trans Neural Netw Learn Syst, 2017, 28: 2826–C2830MathSciNetCrossRefGoogle Scholar
  18. 18.
    Liu X, Cao J, Yu W, et al. Nonsmooth finite-time synchronization of switched coupled neural networks. IEEE Trans Cybern, 2016, 46: 2360–C2371CrossRefGoogle Scholar
  19. 19.
    Yang X, Ho D W C. Synchronization of delayed memristive neural networks: Robust analysis approach. IEEE Trans Cybern, 2016, 46: 3377–C3387CrossRefGoogle Scholar
  20. 20.
    Liu H, Wang Z, Shen B, et al. Event-triggered H state estimation for delayed stochastic memristive neural networks with missing measure- ments: The discrete time case. IEEE Trans Neural Netw Learn Syst, 2017, PP: 1–C12Google Scholar
  21. 21.
    Yang X S, Cao J D, Xu C, et al. Finite-time stabilization of switched dynamical networks with quantized couplings via quantized controller. Sci China Tech Sci, 2018, 61: 299–C308CrossRefGoogle Scholar
  22. 22.
    Aihara K, Takabe T, Toyoda M. Chaotic neural networks. Phys Lett A, 1990, 144: 333–C340MathSciNetCrossRefGoogle Scholar
  23. 23.
    Ashmore J F, Attwell D. Models for electrical tuning in hair cells. Proc R Soc B-Biol Sci, 1985, 226: 325–C344CrossRefGoogle Scholar
  24. 24.
    Koch C. Cable theory in neurons with active, linearized membranes. Biol Cybern, 1984, 50: 15–C33CrossRefGoogle Scholar
  25. 25.
    Babcock K L, Westervelt R M. Stability and dynamics of simple elec- tronic neural networks with added inertia. Phys D-Nonlinear Phenom, 1986, 23: 464–C469CrossRefGoogle Scholar
  26. 26.
    Cao J, Wan Y. Matrix measure strategies for stability and synchroniza- tion of inertial BAM neural network with time delays. Neural Net-works, 2014, 53: 165–C172CrossRefzbMATHGoogle Scholar
  27. 27.
    Qi J, Li C, Huang T. Stability of inertial BAM neural network with time-varying delay via impulsive control. Neurocomputing, 2015, 161: 162–C167CrossRefGoogle Scholar
  28. 28.
    Rakkiyappan R, Premalatha S, Chandrasekar A, et al. Stability and synchronization analysis of inertial memristive neural networks with time delays. Cogn Neurodyn, 2016, 10: 437–C451CrossRefGoogle Scholar
  29. 29.
    Yu S, Zhang Z, Quan Z. New global exponential stability conditions for inertial Cohen-Grossberg neural networks with time delays. Neurocomputing, 2015, 151: 1446–C1454CrossRefGoogle Scholar
  30. 30.
    Xiao Q, Huang Z, Zeng Z. Passivity analysis for memristor-based inertial neural networks with discrete and distributed delays. IEEE Trans Syst Man Cybern Syst, 2017, PP: 1–C11Google Scholar
  31. 31.
    Filippov A F. Differential equations with discontinuous right-hand side. Mat Sb, 1960, 51: 99–C128MathSciNetzbMATHGoogle Scholar
  32. 32.
    Aubin J P, Cellina A. Differential Inclusions. Berlin: Springer-Verlag, 1984CrossRefzbMATHGoogle Scholar
  33. 33.
    Lu W, Chen T. Dynamical behaviors of delayed neural network systems with discontinuous activation functions. Neural Comput, 2006, 18: 683–C708MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Cao J. An estimation of the domain of attraction and convergence rate for Hopfield continuous feedback neural networks. Phys Lett A, 2004, 325: 370–C374MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Chai Wah Wu, Chua L O. Synchronization in an array of linearly coupled dynamical systems. IEEE Trans Circuits Syst I, 1995, 42: 430–C447MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Halanay A. Differential Equations: Stability, Oscillations, Time Lags. New York: Academic Press, 1966zbMATHGoogle Scholar
  37. 37.
    Boyd S, Ghaoui L E, Feron E, et al. Linear Matrix Inequalities in System and Control Theory. Philadelphia: SIAM, 1994Google Scholar
  38. 38.
    Cao J, Li R. Fixed-time synchronization of delayed memristor-based recurrent neural networks. Sci China Inf Sci, 2017, 60: 032201CrossRefGoogle Scholar
  39. 39.
    Huang X, Fan Y, Jia J, et al. Quasi-synchronisation of fractional-order memristor-based neural networks with parameter mismatches. IET Control Theory Appl, 2017, 11: 2317–C2327MathSciNetCrossRefGoogle Scholar
  40. 40.
    Zhang W, Huang T, He X, et al. Global exponential stability of inertial memristor-based neural networks with time-varying delays and impulses. Neural Networks, 2017, 95: 102–C109CrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Mathematics and Information ScienceHenan University of Economics and LawZhengzhouChina
  2. 2.School of Mathematics, and Research Center for Complex Systems and Network SciencesSoutheast UniversityNanjingChina

Personalised recommendations