[go: up one dir, main page]

Skip to main content
Log in

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

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Chua LO (1971) Memristor-the missing circut element. IEEE Trans Circuit Theory 18:507–519

    Article  Google Scholar 

  2. Chua LO, Kang SM (1976) Memristive devices and systems. Proc IEEE 64:209–223

    Article  MathSciNet  Google Scholar 

  3. Strukov DB, Snider GS, Stewart DR, Williams RS (2008) The missing memristor found. Nature 453:80–83

    Article  Google Scholar 

  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 85:157–164

    Article  Google Scholar 

  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 13:815–826

    MathSciNet  MATH  Google Scholar 

  6. Chen S, Cao J (2012) Projective synchronization of neural networks with mixed time-varying delays and parameter mismatch. Nonlinear Dyn 67:1397–1406

    Article  MathSciNet  MATH  Google Scholar 

  7. Haykin S (1998) Neural networks: a comprehensive foundation. Prentice-Hall, Englewood Cliffs

    MATH  Google Scholar 

  8. Yang X, Cao J (2014) Hybrid adaptive and impulsive synchronization of uncertain complex networks with delays and general uncertain perturbations. Appl Math Comput 227:480–493

    MathSciNet  MATH  Google Scholar 

  9. Zhang X, Lv X, Li X (2017) Sampled-data-based lag synchronization of chaotic delayed neural networks with impulsive control. Nonlinear Dyn 90:2199–2207

    Article  MathSciNet  MATH  Google Scholar 

  10. Song Q, Cao J (2008) Dynamical behaviors of discrete-time fuzzy cellular neural networks with variable delays and impulses. J Franklin Inst 345:39–59

    Article  MathSciNet  MATH  Google Scholar 

  11. Yang X, Lu J (2016) Finite-time synchronization of coupled networks with Markovian topology and impulsive effects. IEEE Trans Autom Control 61:2256–2261

    Article  MathSciNet  MATH  Google Scholar 

  12. Lu J, Ho DWC (2011) Stabilization of complex dynamical networks with noise disturbance under performance constraint. Nonlinear Anal Ser B Real World Appl 12:1974–1984

    Article  MathSciNet  MATH  Google Scholar 

  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 129:2029–2035

    Google Scholar 

  14. Lu J, Ding C, Lou J, Cao J (2015) Outer synchronization of partially coupled dynamical networks via pinning impulsive controllers. J Franklin Inst 352:5024–5041

    Article  MathSciNet  MATH  Google Scholar 

  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 351:4435–4456

    Article  MathSciNet  MATH  Google Scholar 

  16. Lu J, Ho DWC (2010) Globally exponential synchronization and synchronizability for general dynamical networks. IEEE Trans Syst Man Cybern 40:350–361

    Article  Google Scholar 

  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 6:35624–35630

    Article  Google Scholar 

  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 24:1701–1707

    Article  Google Scholar 

  19. Li Y, Lou J, Wang Z, Alsaadi FE (2018) Synchronization of nonlinearly coupled dynamical networks under hybrid pinning impulsive controllers. J Franklin Inst 355:6520–6530

    Article  MathSciNet  MATH  Google Scholar 

  20. Li Y, Zhong J, Lu J, Wang Z (2018) On robust synchronization of drive-response boolean control networks with disturbances. Math Probl Eng. https://doi.org/10.1155/2018/1737685

  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 22:1250176

    Article  MATH  Google Scholar 

  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 48:577–601

    Article  Google Scholar 

  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 28:1878–1888

    Article  MathSciNet  Google Scholar 

  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 354:3021–3038

    Article  MathSciNet  MATH  Google Scholar 

  25. Wang J, Wu H, Huang T (2015) Passivity-based synchronization of a class of complex dynamical networks with time-varying delay. Automatica 56:105–112

    Article  MathSciNet  MATH  Google Scholar 

  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 29:618–630

    Article  MathSciNet  Google Scholar 

  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 7:157–169

    Article  Google Scholar 

  28. Zhang L, Yang Y (2018) Different impulsive effects on synchronization of fractional-order memristive BAM neural networks. Nonlinear Dyn. https://doi.org/10.1007/s11071-018-4188-z

    MATH  Google Scholar 

  29. Zhang L, Yang Y, Wang F (2017) Lag synchronization for fractional-order memristive neural networks via period intermittent control. Nonlinear Dyn 89:367–381

    Article  MATH  Google Scholar 

  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 5:827–844

    Article  MathSciNet  MATH  Google Scholar 

  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 43:49–63

    Article  Google Scholar 

  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 28:2924–2935

    Article  MathSciNet  Google Scholar 

  33. Boyd S, Ghaoui LE, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM, Philadelphia

    Book  MATH  Google Scholar 

  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. https://doi.org/10.1155/2017/8314757

    MathSciNet  Google Scholar 

  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 29:3726–3737

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xingbao Gao.

Ethics declarations

Conflict of Interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This work was supported by National Natural Science Foundation of China (Grant Nos. 61803247, 61802243, 61273311 and 61173094), Project Funded by China Postdoctoral Science Foundation 2018M640948, the Fundamental Research Funds for the Central Universities under Grant No. GK201903003, the Jiangsu Provincial Key Laboratory of Networked Collective Intelligence under Grant No. BM2017002.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, R., Gao, X. & Cao, J. Exponential Synchronization of Stochastic Memristive Neural Networks with Time-Varying Delays. Neural Process Lett 50, 459–475 (2019). https://doi.org/10.1007/s11063-019-09989-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-019-09989-5

Keywords

Navigation