Exponential Synchronization of Stochastic Memristive Neural Networks with Time-Varying Delays

  • Ruoxia Li
  • Xingbao GaoEmail author
  • Jinde Cao


This paper pays attention to the synchronization control methodology for stochastic memristive system. On the framework of Lyapunov functional, stability theory and free-weighting matrices technique, some brand-new solvability criteria are established to ensure the exponential synchronization goal of the target model. Considering the introduce of some free-weighting matrices, the obtained synchronization verdict will be much more applicable. Finally, the living example is included to show the effectiveness of the presented methodology.


Exponential synchronization Memristive neural networks Stochastic terms Robust technique 


Compliance with ethical standards

Conflict of Interest

The authors declare that they have no conflict of interest.


  1. 1.
    Chua LO (1971) Memristor-the missing circut element. IEEE Trans Circuit Theory 18:507–519CrossRefGoogle Scholar
  2. 2.
    Chua LO, Kang SM (1976) Memristive devices and systems. Proc IEEE 64:209–223MathSciNetCrossRefGoogle Scholar
  3. 3.
    Strukov DB, Snider GS, Stewart DR, Williams RS (2008) The missing memristor found. Nature 453:80–83CrossRefGoogle Scholar
  4. 4.
    Yang X, Feng Z, Feng J, Cao J (2017) Synchronization of discrete-time neural networks with delays and Markov jump topologies based on tracker information. Neural Netw 85:157–164CrossRefGoogle Scholar
  5. 5.
    Cohen MA, Grossberg S (1987) Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans Systems Man Cybern 13:815–826MathSciNetzbMATHGoogle Scholar
  6. 6.
    Chen S, Cao J (2012) Projective synchronization of neural networks with mixed time-varying delays and parameter mismatch. Nonlinear Dyn 67:1397–1406MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Haykin S (1998) Neural networks: a comprehensive foundation. Prentice-Hall, Englewood CliffszbMATHGoogle Scholar
  8. 8.
    Yang X, Cao J (2014) Hybrid adaptive and impulsive synchronization of uncertain complex networks with delays and general uncertain perturbations. Appl Math Comput 227:480–493MathSciNetzbMATHGoogle Scholar
  9. 9.
    Zhang X, Lv X, Li X (2017) Sampled-data-based lag synchronization of chaotic delayed neural networks with impulsive control. Nonlinear Dyn 90:2199–2207MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Song Q, Cao J (2008) Dynamical behaviors of discrete-time fuzzy cellular neural networks with variable delays and impulses. J Franklin Inst 345:39–59MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Yang X, Lu J (2016) Finite-time synchronization of coupled networks with Markovian topology and impulsive effects. IEEE Trans Autom Control 61:2256–2261MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Lu J, Ho DWC (2011) Stabilization of complex dynamical networks with noise disturbance under performance constraint. Nonlinear Anal Ser B Real World Appl 12:1974–1984MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Wang Z, Ding S, Huang Z, Zhang H (2015) Exponential stability and stabilization of delayed memristive neural networks based on quadratic convex combination method. IEEE Trans Neural Netw Learn Syst 129:2029–2035Google Scholar
  14. 14.
    Lu J, Ding C, Lou J, Cao J (2015) Outer synchronization of partially coupled dynamical networks via pinning impulsive controllers. J Franklin Inst 352:5024–5041MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Li X, Zhu Q, O’Regan D (2014) pth Moment exponential stability of impulsive stochastic functional differential equations and application to control problems of NNs. J Franklin Inst 351:4435–4456MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Lu J, Ho DWC (2010) Globally exponential synchronization and synchronizability for general dynamical networks. IEEE Trans Syst Man Cybern 40:350–361CrossRefGoogle Scholar
  17. 17.
    Li Y, Li B, Liu Y, Lu J, Wang Z, Alsaadi F (2018) Set stability and set stabilization of switched Boolean networks with state-based switching. IEEE Access 6:35624–35630CrossRefGoogle Scholar
  18. 18.
    Zhang G, Shen Y (2013) New algebraic criteria for synchronization stability of chaotic memristive neural networks with time-varying delays. IEEE Trans Neural Netw Learn Syst 24:1701–1707CrossRefGoogle Scholar
  19. 19.
    Li Y, Lou J, Wang Z, Alsaadi FE (2018) Synchronization of nonlinearly coupled dynamical networks under hybrid pinning impulsive controllers. J Franklin Inst 355:6520–6530MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Li Y, Zhong J, Lu J, Wang Z (2018) On robust synchronization of drive-response boolean control networks with disturbances. Math Probl Eng.
  21. 21.
    Lu J, Wang Z, Cao J, Ho DWC, Kurths J (2012) Pinning impulsive stabilization of nonlinear dynamical networks with time-varying delay. Int J Bifurc Chaos 22:1250176CrossRefzbMATHGoogle Scholar
  22. 22.
    Yan M, Qiu J, Chen X, Chen X, Yang C, Zhang A, Alsaadi F (2018) The global exponential stability of the delayed complex-valued neural networks with almost periodic coefficients and discontinuous activations. Neural Process Lett 48:577–601CrossRefGoogle Scholar
  23. 23.
    Yang X, Cao J, Liang J (2017) Exponential synchronization of memristive neural networks with delays: interval matrix method. IEEE Trans Neural Netw Learn Syst 28:1878–1888MathSciNetCrossRefGoogle Scholar
  24. 24.
    Li R, Cao J, Alsaedi A, Ahmad B (2017) Passivity analysis of delayed reaction-diffusion Cohen–Grossberg neural networks via Hardy-Poincarè inequality. J Franklin Inst 354:3021–3038MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Wang J, Wu H, Huang T (2015) Passivity-based synchronization of a class of complex dynamical networks with time-varying delay. Automatica 56:105–112MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Ding S, Wang Z, Zhang H (2018) Dissipativity analysis for stochastic memristive neural networks with time-varying delays: a discrete-time case. IEEE Trans Neural Netw Learn Syst 29:618–630MathSciNetCrossRefGoogle Scholar
  27. 27.
    Li R, Wei H (2016) Synchronization of delayed Markovian jump memristive neural networks with reaction-diffusion terms via sampled data control. Int J Mach Learn Cybern 7:157–169CrossRefGoogle Scholar
  28. 28.
    Zhang L, Yang Y (2018) Different impulsive effects on synchronization of fractional-order memristive BAM neural networks. Nonlinear Dyn. zbMATHGoogle Scholar
  29. 29.
    Zhang L, Yang Y, Wang F (2017) Lag synchronization for fractional-order memristive neural networks via period intermittent control. Nonlinear Dyn 89:367–381CrossRefzbMATHGoogle Scholar
  30. 30.
    Li R, Wu H, Zhang X, Yao R (2015) Adaptive projective synchronization of memristive neural networks with time-varying delays and stochastic perturbation. Math Control Relat Fields 5:827–844MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Wang W, Li L, Peng H, Kurths J, Xiao J, Yang Y (2016) Finite-time anti-synchronization control of memristive neural networks with stochastic perturbations. Neural Process Lett 43:49–63CrossRefGoogle Scholar
  32. 32.
    Li R, Cao J (2016) Finite-time stability analysis for markovian jump memristive neural networks with partly unknown transition probabilities. IEEE Trans Neural Netw Learn Syst 28:2924–2935MathSciNetCrossRefGoogle Scholar
  33. 33.
    Boyd S, Ghaoui LE, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM, PhiladelphiaCrossRefzbMATHGoogle Scholar
  34. 34.
    Yu M, Wang W, Luo X, Liu L, Yuan M (2017) Exponential antisynchronization control of stochastic memristive neural networks with mixed time-varying delays based on novel delay-dependent or delay-independent adaptive controller. Math Probl Eng. MathSciNetGoogle Scholar
  35. 35.
    Liu H, Wang Z, Shen B, Liu X (2017) Event-triggered \(H_\infty \) state estimation for delayed stochastic memristive neural networks with missing measurements: the discrete time case. IEEE Trans Neural Netw Learn Syst 29:3726–3737MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematics and Information ScienceShaanxi Normal UniversityXi’anChina
  2. 2.The Jiangsu Provincial Key Laboratory of Networked Collective Intelligence, and School of MathematicsSoutheast UniversityNanjingChina

Personalised recommendations