Skip to main content
SpringerLink
Log in

New Algebraic Criteria for Global Exponential Periodicity and Stability of Memristive Neural Networks with Variable Delays

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

This paper concentrates on the problem of global exponential periodicity and stability of memristive neural networks with variable delays. By constructing the appropriate Lyapunov functionals and utilizing some inequality techniques, new algebraic criteria are proposed to guarantee the existence and global exponential stability of periodic solution of the considered system. In addition, the proposed theoretical results not only expand and complement the earlier publications, but also are easy to be checked with the parameters of system itself. A numerical example is given to demonstrate the effectiveness of our results.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

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

    Article  Google Scholar 

  2. Strukov D, Snider G, Stewart G, Williams R (2008) The missing memristor found. Nature 453:80–83

    Article  Google Scholar 

  3. Tour J, He T (2008) The fourth element. Nature 453:42–43

    Article  Google Scholar 

  4. Gao L, Alibart F, Strukov D (2013) Programmable CMOS/memristor threshold logic. IEEE Trans Nanotechnol 12(2):115–119

    Article  Google Scholar 

  5. Itoh M, Chua L (2009) Memristor cellular automata and memristor discrete-time cellular neural networks. Int J Bifurc Chaos 19:3605–3656

    Article  Google Scholar 

  6. Corinto F, Ascoli A, Gilli M (2011) Nonlinear dynamics of memristor oscillators. IEEE Trans Circuit Syst 58:1323–1336

    Article  MathSciNet  Google Scholar 

  7. Zhang Y, Shen Y, Wang X, Cao L (2015) A novel design for memristor-based logic switch and crossbar circuits. IEEE Trans Circuits Syst 62:1402–1411

    Article  Google Scholar 

  8. Cantley K, Subramaniam A, Stiegler H, Chapman R, Vogel E (2011) Hebbian learning in spiking neural networks with nanocrystalline silicon TFTs and memristive synapses. IEEE Trans Nanotechnol 10:1066–1073

    Article  Google Scholar 

  9. Sun J, Shen Y (2015) Quasi-ideal memory system. IEEE Trans Cybern 45(7):1533–1576

    Article  Google Scholar 

  10. Miller K, Nalwa K, Bergerud A, Neihart N, Chaudhary S (2010) Memristive behavior in thin anodic titania. IEEE Electron Device Lett 31(7):737–739

    Article  Google Scholar 

  11. Wen S, Zeng Z, Huang T, Meng Q, Yao W (2015) Lag synchronization of switched neural networks via neural activation function and applications in image encryption. IEEE Trans Neural Netw Learn Syst 26(7):1493–1502

    Article  MathSciNet  Google Scholar 

  12. Zhu S, Yang Q, Shen Y (2013) Noise further expresses exponential decay for globally exponentially stable time-varying delayed neural networks. Neural Netw 77:7–13

    Article  Google Scholar 

  13. Qi J, Li C, Huang T, Zhang W (2016) Exponential stability of switched time-varying delayed neural networks with all modes being unstable. Neural Process Lett 43:553–565

    Article  Google Scholar 

  14. Wang J, Huang L, Guo Z (2009) Dynamical behavior of delayed Hopfield neural networks with discontinuous activations. Appl Math Model 33:1793–1802

    Article  MathSciNet  Google Scholar 

  15. Xiao J, Zeng Z, Shen W (2015) Passivity analysis of delayed neural networks with discontinuous activations. Neural Process Lett 42:215–232

    Article  Google Scholar 

  16. Gan Q, Liang Y (2012) Synchronization of non-identical unknown chaotic delayed neural networks based on adaptive sliding mode control. Neural Process Lett 35:245–255

    Article  Google Scholar 

  17. Wu A, Liu L, Huang T, Zeng Z (2017) Mittag–Leffler stability of fractional-order neural networks in the presence of generalized piecewise constant arguments. Neural Netw 85:118–127

    Article  Google Scholar 

  18. He X, Huang T, Yu J, Li C, Li C (2017) An inertial projection neural network for solving variational inequalities. IEEE Trans Cybern 47:809–814

    Article  Google Scholar 

  19. Huang T, Li C, Duan S, Starzyk J (2012) Robust exponential stability of uncertain delayed neural networks with stochastic perturbation and impulse effects. IEEE Trans Neural Netw Learn Syst 23:866–875

    Article  Google Scholar 

  20. Hu C, Yu J, Chen Z, Jiang H, Huang T (2017) Fixed-time stability of dynamical systems and fixed-time synchronization of coupled discontinuous neural networks. Neural Netw 89:74–83

    Article  Google Scholar 

  21. Wang J, Wu H, Huang T, Ren S, Wu J (2016) Passivity and output synchronization of complex dynamical networks with fixed and adaptive coupling strength. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2016.2627083

    Article  Google Scholar 

  22. Li C, Yu W, Huang T (2014) Impulsive synchronization schemes of stochastic complex networks with switching topology: average time approach. Neural Netw 54:85–94

    Article  Google Scholar 

  23. Li C, Yu X, Huang T, He X (2017) Distributed optimal consensus over resource allocation network and its application to dynamical economic dispatch. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2017.2691760

    Article  Google Scholar 

  24. Wen S, Zeng Z (2012) Dynamics analysis of a class of memristor-based recurrent networks with time-varying delays in the presence of strong external stimuli. Neural Process Lett 35:47–59

    Article  Google Scholar 

  25. Wu A, Zeng Z (2014) Lagrange stability of neural networks with memristive synapses and multiple delays. Info Sci 280:135–151

    Article  MathSciNet  Google Scholar 

  26. Zhang G, Shen Y, Wang L (2013) Global anti-synchronization of a class of chaotic memristive neural networks with time-varying delays. Neural Netw 46:1–8

    Article  Google Scholar 

  27. Wang H, Duan S, Huang T, Li C, Wang L (2016) Novel stability criteria for impulsive memristive neural networks with time-varying delays. Circuits Syst Signal Process 35:3935–3956

    Article  Google Scholar 

  28. 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(10):1701–1707

    Article  Google Scholar 

  29. Zhang G, Shen Y, Yin Q, Sun J (2013) Global exponential periodicity and stability of a class of memristor-based recurrent neural networks with multiple delays. Info Sci 232:386–396

    Article  MathSciNet  Google Scholar 

  30. Wen S, Huang T, Zeng Z, Chen Y, Li P (2015) Circuit design and exponential stabilization of memristive neural networks. Neural Netw 63:48–56

    Article  Google Scholar 

  31. Wang L, Shen Y, Yin Q, Zhang G (2015) Adaptive synchronization of memristor-based neural networks with time-varying delays. IEEE Trans Neural Netw Learn Syst 26:2033–2042

    Article  MathSciNet  Google Scholar 

  32. 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 25:704–717

    Article  Google Scholar 

  33. Guo Z, Wang J, Yan Z (2013) Global exponential dissipativity and stabilization of memristor-based recurrent neural networks with timevarying delays. Neural Netw 48:158–172

    Article  Google Scholar 

  34. Wang X, Li C, Huang T, Duan S (2014) Global exponential stability of a class of memristive neural networks with time-varying delays. Neural Comput Appl 24:1707–1715

    Article  Google Scholar 

  35. Bao G, Zeng Z (2013) Multistability of periodic delayed recurrent neural network with memristors. Neural Comput Appl 23:1963–1967

    Article  Google Scholar 

  36. Cao J (2003) New results concerning exponential stability and periodic solutions of delayed cellular neural networks. Phys Lett A 307:136–147

    Article  MathSciNet  Google Scholar 

  37. Chen B, Wang J (2005) Global exponential periodicity of a class of recurrent neural networks with oscillating parameters and time-varying delays. IEEE Trans Neural Netw Learn Syst 16:1440–1448

    Article  Google Scholar 

  38. Hong X, Yan K, Wang B (2006) Existence and global exponential stability of periodic solution for delayed high-order Hopfield-type neural networks. Phys Lett A 352:341–349

    Article  Google Scholar 

  39. Liu X, Cao J (2009) On periodic solutions of neural networks via differential inclusions. Neural Netw 22:329–334

    Article  Google Scholar 

  40. Papini D, Taddei V (2005) Global exponential stability of the periodic solution of a delayed neural network with discontinuous activations. Phys Lett A 343:117–128

    Article  Google Scholar 

  41. Zhang W, Li C, Huang T (2015) Exponential stability of inertial BAM neural networks with time-varying delay via periodically intermittent control. Neural Comput Appl 10:1–7

    Google Scholar 

  42. Dugundji J, Grranas A (1986) Fixed point theory. In: Monografie matematyczne, vol 123. PWN, Warsaw

  43. Filippov A (1988) Differential equations with discontinuous right-hand sides. Kluwer, Dordrecht

    Book  Google Scholar 

  44. Xue X, Yu J (2007) Periodic solutions for semi-linear evolution inclusions. J Math Anal Appl 331:1246–1262

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported by the Fundamental Research Funds for the Central Universities (2014XT02).

Author information

Authors and Affiliations

  1. School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, China

    Song Zhu, Dan Liu & Shengwu Zhou

  2. School of Mathematics, Southeast University, Nanjing, 210096, China

    Er Ye

Authors
  1. Song Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Er Ye
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dan Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shengwu Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Song Zhu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhu, S., Ye, E., Liu, D. et al. New Algebraic Criteria for Global Exponential Periodicity and Stability of Memristive Neural Networks with Variable Delays. Neural Process Lett 48, 1749–1766 (2018). https://doi.org/10.1007/s11063-018-9803-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-018-9803-y

Keywords

Search

Navigation