Neural Processing Letters

, Volume 49, Issue 1, pp 103–119 | Cite as

Global Exponential Synchronization of Memristive Competitive Neural Networks with Time-Varying Delay via Nonlinear Control

  • Shuqing Gong
  • Shaofu Yang
  • Zhenyuan GuoEmail author
  • Tingwen Huang


This paper investigates the synchronization problem of memristive competitive neural networks (MCNNs) with time-varying delay. Firstly, a novel nonlinear controller with a linear diffusive term and a discontinuous sign function term is introduced. Then, by using this controller, several sufficient conditions for global exponential synchronization of MCNNs are presented based on Lyapunov stability theory and some inequality techniques. Finally, two illustrative examples are provided to substantiate the effectiveness of the obtained theoretical results.


Global exponential synchronization Memristive Competitive neural network Time-varying delay Nonlinear controller 


  1. 1.
    Bondarenko VE (2005) Information processing, memories, and synchronization in chaotic neural network with the time delay. Complexity 11(2):39–52MathSciNetCrossRefGoogle Scholar
  2. 2.
    Cao J, Wan Y (2014) Matrix measure strategies for stability and synchronization of inertial BAM neural network with time delays. Neural Netw 53:165–172CrossRefzbMATHGoogle Scholar
  3. 3.
    Cao J, Wang J (2004) Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delays. Neural Netw 17(3):379–390MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Chen J, Zeng Z, Jiang P (2014) Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks. Neural Netw 51:1–8CrossRefzbMATHGoogle Scholar
  5. 5.
    Chua LO (1971) Memristor—the missing circuit element. IEEE Trans Circuit Theory 18(5):507–519CrossRefGoogle Scholar
  6. 6.
    Cohen M, Grossberg S (1983) Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans Syst Man Cybern 13(5):815–826MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Collins JJ, Stewart IN (1993) Coupled nonlinear oscillators and the symmetries of animal gaits. J Nonlinear Sci 3(1):349–392MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Duan FT, Cui BT (2015) Synchronization of memristor-based competitive neural networks with different time scales. Appl Mech Mater 740:238–242CrossRefGoogle Scholar
  9. 9.
    Duan L, Huang L (2014) Periodicity and dissipativity for memristor-based mixed time-varying delayed neural networks via differential inclusions. Neural Netw 57:12–22CrossRefzbMATHGoogle Scholar
  10. 10.
    Duan L, Huang L, Fang X (2017) Finite-time synchronization for recurrent neural networks with discontinuous activations and time-varying delays. Chaos 27(1):013101MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Duan L, Huang L, Guo Z, Fang X (2017) Periodic attractor for reaction-diffusion high-order Hopfield neural networks with time-varying delays. Comput Math Appl 73(2):233–245MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Duane GS, Webster PJ, Weiss JB (1999) Co-occurrence of northern and southern hemisphere blocks as partially synchronized chaos. J Atmos Sci 56(24):4183–4205CrossRefGoogle Scholar
  13. 13.
    Feng J, Ma Q, Qin S (2017) Exponential stability of periodic solution for impulsive memristor-based Cohen–Grossberg neural networks with mixed delays. Int J Pattern Recognit Artif Intell 31(07):1750022MathSciNetCrossRefGoogle Scholar
  14. 14.
    Gan Q, Hu R, Liang Y (2012) Adaptive synchronization for stochastic competitive neural networks with mixed time-varying delays. Commun Nonlinear Sci Numer Simul 17(9):3708–3718MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Gan Q, Xu RX, Kang X (2012) Synchronization of unknown chaotic delayed competitive neural networks with different time scales based on adaptive control and parameter identification. Nonlinear Dyn 67(3):1893–1902MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Gu H (2009) Adaptive synchronization for competitive neural networks with different time scales and stochastic perturbation. Neurocomputing 73(1):350–356CrossRefGoogle Scholar
  17. 17.
    Guo Z, Wang J, Yan Z (2014) Attractivity analysis of memristor-based cellular neural networks with time-varying delays. IEEE Trans Neural Netw Learn Syst 25(4):704–717CrossRefGoogle Scholar
  18. 18.
    Guo Z, Wang J, Yan Z (2015) Global exponential synchronization of two memristor-based recurrent neural networks with time delays via static or dynamic coupling. IEEE Trans Syst Man Cybern Syst 45(2):235–249CrossRefGoogle Scholar
  19. 19.
    Guo Z, Yang S, Wang J (2015) Global exponential synchronization of multiple memristive meural metworks with time delay via nonlinear coupling. IEEE Trans Neural Netw Learn Syst 26(6):1300–1311MathSciNetCrossRefGoogle Scholar
  20. 20.
    Guo Z, Yang S, Wang J (2016) Global synchronization of stochastically disturbed memristive neurodynamics via discontinuous control laws. IEEE/CAA J Autom Sin 3(2):121–131MathSciNetCrossRefGoogle Scholar
  21. 21.
    Itoh M, Chua LO (2009) Memristor cellular automata and memristor discrete-time cellular neural networks. Int J Bifurcat Chaos 19(11):3605–3656CrossRefzbMATHGoogle Scholar
  22. 22.
    Kim H, Sah MP, Yang C, Roska T (2012) Neural synaptic weighting with a pulse-based memristor circuit. IEEE Trans Circuits Syst I Regul Pap 59(1):148–158MathSciNetCrossRefGoogle Scholar
  23. 23.
    Li Y, Yang X, Shi L (2016) Finite-time synchronization for competitive neural networks with mixed delays and non-identical perturbations. Neurocomputing 185:242–253CrossRefGoogle Scholar
  24. 24.
    Liao TL, Huang N (1999) An observer-based approach for chaotic synchronization with applications to secure communications. IEEE Trans Circuits Syst I Fundam Theory Appl 46(9):1144–1150CrossRefzbMATHGoogle Scholar
  25. 25.
    Lu J, Zhong J, Ho DWC, Cao J (2016) On controllability of delayed Boolean control networks. Siam J Control Optim 54(2):475–494MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Lu J, Li H, Liu Y, Li F (2017) Survey on semi-tensor product method with its applications in logical networks and other finite-valued systems. IET Control Theory Appl 11(13):2040–2047MathSciNetCrossRefGoogle Scholar
  27. 27.
    Ma Q, Pan X, Qin S (2016) Global asymptotic stability of anti-periodic solution for impulsive Cohen–Grossberg neural networks with multiple delays. In: Intelligent control and information processing (ICICIP) seventh international conference on IEEE, vol 2016, pp 229–235Google Scholar
  28. 28.
    Meyer-Bäse A, Ohl F, Scheich H (1996) Singular perturbation analysis of competitive neural networks with different time-scales. Neural Comput 8(8):1731–1742CrossRefGoogle Scholar
  29. 29.
    Nie X, Cao J (2011) Multistability of second-order competitive neural networks with nondecreasing saturated activation functions. IEEE Trans Neural Netw 22(11):1694–1708CrossRefGoogle Scholar
  30. 30.
    Nie X, Huang Z (2012) Multistability and multiperiodicity of high-order competitive neural networks with a general class of activation functions. Neurocomputing 82:1–13CrossRefGoogle Scholar
  31. 31.
    Sharifi MJ, Banadaki YM (2010) General spice models for memristor and application to circuit simulation of memristor-based synapses and memory cells. J Circuits Syst Comput 19(02):407–424CrossRefGoogle Scholar
  32. 32.
    Shi Y, Zhu P (2014) Synchronization of memristive competitive neural networks with different time scales. Neural Comput Appl 25(5):1163–1168CrossRefGoogle Scholar
  33. 33.
    Strukov DB, Snider GS, Stewart DR (2008) The missing memristor found. Nature 453(7191):80–83CrossRefGoogle Scholar
  34. 34.
    Xin Y, Li Y, Cheng Z, Huang X (2016) Global exponential stability for switched memristive neural networks with time-varying delays. Neural Netw 80:34–42CrossRefzbMATHGoogle Scholar
  35. 35.
    Yang X, Cao J, Long Y, Rui W (2010) Adaptive lag synchronization for competitive neural networks with mixed delays and uncertain hybrid perturbations. IEEE Trans Neural Netw 21(10):1656–1667CrossRefGoogle Scholar
  36. 36.
    Yang X, Huang C, Cao J (2012) An LMI approach for exponential synchronization of switched stochastic competitive neural networks with mixed delays. Neural Comput Appl 21(8):2033–2047CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Mathematics and EconometricsHunan UniversityChangshaChina
  2. 2.School of Computer Science and EngineeringSoutheast UniversityNanjingChina
  3. 3.Science ProgramTexas A&M University at QatarDohaQatar

Personalised recommendations