Skip to main content
SpringerLink
Log in

Exponential stability analysis for delayed complex-valued memristor-based recurrent neural networks

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

The exponential stability problem for complex-valued memristor-based recurrent neural networks (CVMRNNs) with time delays is studied in this paper. As an extension of real-valued memristor-based recurrent neural networks, CVMRNNs can be separated into real and imaginary parts and an equivalent real-valued system is formed. By constructing a novel Lyapunov function, a new sufficient condition to guarantee the existence, uniqueness, and global exponential stability of the equilibrium point for complex-valued systems is given in terms of M-matrix. The effectiveness of the theoretical result is shown by two numerical examples.

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

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

References

  1. Lee DL (2001) Improving the capacity of complex-valued neural networks with a modified gradient descent learning rule. IEEE Trans Neural Netw 12(2):439–443

    Article  Google Scholar 

  2. Hirose A (2006) Complex-Valued Neural Networks. Springer, New York

    Book  MATH  Google Scholar 

  3. Hirose A (2012) Advances in applications of complex-valued neural networks. J Soc Instrum Control Eng 251(4):351–357

    Google Scholar 

  4. Hirose A, Yoshida S (2012) Generalization characteristics of complex-valued feedforward neural networks in relation to signal coherence. IEEE Trans Neural Netw Learn Syst 23(4):541–551

    Article  Google Scholar 

  5. Kuroe Y, Hashimoto N, Mori T (2002) On energy function for complex-valued neural networks and its applications. In: Proceedings of 9th International Conference on Neural Information Processing, pp 1079-1083

  6. Muezzinoglu MK, Cuzelis C, Zurada JM (2003) A new design method for the complex-valued multistate hopfield associative memory. IEEE Trans Neural Netw 14(4):891–899

    Article  Google Scholar 

  7. Goh SL, Mandic DP (2007) An augmented extended Kalman filter algorithm for complex-valued recurrent neural networks. Neural Comput 19:1039–1055

    Article  MATH  Google Scholar 

  8. Rao VSH, Murthy GR (2008) Global dynamics of a class of complex valued neural networks. Int J Neural Syst 18(2):165–171

    Article  Google Scholar 

  9. Kobayashi M (2010) Exceptional reducibility of complex-valued neural networks. IEEE Trans Neural Netw 21(7):1060–1072

    Article  Google Scholar 

  10. Nitta T (2009) Complex-Valued Neural Networks: Utilizing High-Dimensional Parameters. Information Science Reference, New York

    Book  Google Scholar 

  11. Hu J, Wang J (2012) Global stability of complex-valued recurrent neural networks with time-delays. IEEE Trans Neural Netw Learn Syst 23(6):853–865

    Article  Google Scholar 

  12. Zhou B, Song Q (2013) Boundedness and complete stability of complex-valued neural networks with time delay. IEEE Trans Neural Netw Learn Syst 24(8):1227–1238

    Article  Google Scholar 

  13. Valle ME (2014) Complex-valued recurrent correlation neural networks. IEEE Trans Neural Netw Learn Syst 25(9):1600–1612

    Article  Google Scholar 

  14. Zhang Z, Lin C, Chen B (2014) Global stability criterion for delayed complex-valued recurrent neural networks. IEEE Trans Neural Netw Learn Syst 25(9):1704–1708

    Article  Google Scholar 

  15. Fang T, Sun J (2014) Further investigate the stability of complex-valued recurrent neural networks with time-delays. IEEE Trans Neural Netw Learn Syst 25(9):1709–1713

    Article  Google Scholar 

  16. Xu X, Zhang J, Shi J (2017) Dynamical behaviour analysis of delayed complex-valued neural networks with impulsive effect. Int J Syst Sci 48(4):686–694. doi:10.1080/00207721.2016.1206988

    Article  MathSciNet  MATH  Google Scholar 

  17. Ma Q, Feng G, Xu S (2013) Delay-dependent stability criteria for reaction–diffusion neural networks with time-varying delays. IEEE Trans Cybern 43(6):1913–1920

    Article  Google Scholar 

  18. Gong W, Liang J, Cao J (2015) Matrix measure method for global exponential stability of complex-valued recurrent neural networks with time-varying delays. Neural Netw 70:81–89

    Article  MATH  Google Scholar 

  19. Liu X, Chen T (2016) Global exponential stability for complex-valued recurrent neural networks with asynchronous time delays. IEEE Trans Neural Netw Learn Syst 27(3):593–606

    Article  MathSciNet  Google Scholar 

  20. Rakkiyappan R, Cao J, Velmurugan G (2015) Existence and uniform stability analysis of fractional-order complex-valued neural networks with time delays. IEEE Trans Neural Netw Learn Syst 26(1):84–97

    Article  MathSciNet  MATH  Google Scholar 

  21. Li X, Song S (2013) Impulsive control for existence, uniqueness and global stability of periodic solutions of recurrent neural networks with discrete and continuously distributed delays. IEEE Trans Neural Netw 24:868–877

    Article  Google Scholar 

  22. Li X, Song S (2014) Research on synchronization of chaotic delayed neural networks with stochastic perturbation using impulsive control method. Commun Nonlinear Sci 19(10):3892–3900

    Article  MathSciNet  Google Scholar 

  23. Velmurugan G, Rakkiyappan R, Cao J (2015) Further analysis of global \(\mu\)-stability of complex-valued neural networks with unbounded time-varying delays. Neural Netw 67:14–27

    Article  MATH  Google Scholar 

  24. Dong T, Liao X, Wang A (2015) Stability and Hopf bifurcation of a complex-valued neural network with two time delays. Nonlinear Dyn 82:173–184

    Article  MathSciNet  MATH  Google Scholar 

  25. Huang Y, Zhang H, Wang Z (2014) Multistability of complex-valued recurrent neural networks with real- imaginary-type activation functions. Appl Math Comput 229:187–200

    Article  MathSciNet  MATH  Google Scholar 

  26. Li Y, Liao X, Li H (2016) Global attracting sets of nonautonomous and complex-valued neural networks with time-varying delays. Neurocomputing 173(3):994–1000

    Article  Google Scholar 

  27. Song Q, Zhao Z (2016) Stability criterion of complex-valued neural networks with both leakage delay and time-varying delays on time scales. Neurocomputing 171:179–184

    Article  Google Scholar 

  28. Ma Q, Xu S, Lewis F, Zhang B, Zou Y (2016) Cooperative output regulation of singular heterogeneous multiagent systems. IEEE Trans Cybern 46(6):1471–1475

    Article  Google Scholar 

  29. Song Q, Yan H, Zhao Z, Liu Y (2016) Global exponential stability of impulsive complex-valued neural networks with both asynchronous time-varying and continuously distributed delays. Neural Netw 81:1–10

    Article  MATH  Google Scholar 

  30. Gong W, Liang J, Zhang C (2016) Multistability of complex-valued neural networks with distributed delays. Neural Comput Appl. doi:10.1007/s00521-016-2305-9

  31. Xie D, Jiang Y (2016) Global exponential stability of periodic solution for delayed complex-valued neural networks with impulses. Neurocomputing 207(528):538

    Google Scholar 

  32. 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 Frankl Inst 351:4435–4456

    Article  MATH  Google Scholar 

  33. Li X, Zhu Q, O’Regan D, Akca H (2015) Global exponential stabilization of impulsive neural networks with unbounded continuously distributed delays. IMA J Appl Math 80(1):85–99

    Article  MathSciNet  MATH  Google Scholar 

  34. Pan J, Liu X, Xie W (2015) Exponential stability of a class of complex-valued neural networks with time- varying delays. Neurocomputing 164:293–299

    Article  Google Scholar 

  35. Chua LO (1971) Memristor-the missing circuit element. IEEE Trans Circuit Theory 18(5):507–519

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  38. Itoh M, Chua LO (2009) Memristor cellular automata and memristor discrete-time cellular neural networks. Int J Bifurcation Chaos 19(11):3605–3656

    Article  MATH  Google Scholar 

  39. Ebong IE, Mazumder P (2011) Self-controlled writing and erasing in a memristor crossbar memory. IEEE Trans Nanotechnol 10(6):1454–1463

    Article  Google Scholar 

  40. Hu J, Wang J (2010) Global uniform asymptotic stability of memristor-based recurrent neural networks with time delays. In: Proceedings of International Joint Conference on Neural Networks, pp 1-8

  41. Mathiyalagan K, Anbuvithya R, Sakthivel R, Park JH, Prakash P (2016) Non-fragile \(H_\infty\) synchronization of memristor-based neural networks using passivity theory. Neural Netw 74:85–100

    Article  MATH  Google Scholar 

  42. 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):704–717

    Article  Google Scholar 

  43. Velmurugan G, Rakkiyappan R (2016) Hybrid projective synchronization of fractional-order memristor-based neural networks with time delays. Nonlinear Dyn 83:419–432

    Article  MathSciNet  MATH  Google Scholar 

  44. Wang Z, Ding S, Huang Z, Zhang H (2016) Exponential stability and stabilization of delayed memristive neural networks based on quadratic convex combination method. IEEE Trans Neural Netw Learn Syst 27(11):2337–2350

    Article  Google Scholar 

  45. 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  MATH  Google Scholar 

  46. Rakkiyappan R, Velmurugan G, Cao J (2014) Finite-time stability analysis of fractional-order complex-valued memristor-based neural networks with time delays. Nonlinear Dyn 78(4):2823–2836

    Article  MathSciNet  MATH  Google Scholar 

  47. Rakkiyappan R, Velmurugan G, Cao J (2015) Stability analysis of memristor-based fractional-order neural networks with different memductance functions. Cogn Neurodyn 9:145–177

    Article  Google Scholar 

  48. Wei H, Li R, Chen C, Tu Z (2017) Stability analysis of fractional order complex-valued memristive neural networks with time delays. Neural Process Lett 45(2):379–399. doi:10.1007/s11063-016-9531-0

    Article  Google Scholar 

  49. Rakkiyappan R, Sivaranjani K, Velmurugan G (2014) Passivity and passification of memristor-based complex-valued recurrent neural networks with interval time-varying delays. Neurocomputing 144:391–407

    Article  Google Scholar 

  50. Velmurugan G, Rakkiyappan R, Lakshmanan S (2015) Passivity analysis of memristor-based complex-valued neural networks with time-varying delays. Neural Process Lett 42:517–540

    Article  Google Scholar 

  51. Li X, Rakkiyappan R, Velmurugan G (2015) Dissipativity analysis of memristor-based complex-valued neural networks with time-varying delays. Inf Sci 294:645–665

    Article  MathSciNet  MATH  Google Scholar 

  52. Rakkiyappan R, Velmurugan G, Li X, O’Regan D (2016) Global dissipativity of memristor-based complex-valued neural networks with time-varying delays. Neural Comput Appl 27:629–649

    Article  Google Scholar 

  53. Rakkiyappan R, Velmurugan G, Rihan FA, Lakshmanan S (2016) Stability analysis of memristor-based complex-valued recurrent neural networks with time delays. Complexity 21:14–39

    Article  MathSciNet  Google Scholar 

  54. Wang H, Duan S, Huang T, Wang L, Li C (2017) Exponential stability of complex-valued memristive recurrent neural networks. IEEE Trans Neural Netw Learn Syst 28(3):766–771. doi:10.1109/TNNLS.2015.2513001

    Article  Google Scholar 

  55. Filippov AF (1988) Differential Equations With Discontinuous Righthand Sides. Kluwer, Dordrecht

    Book  Google Scholar 

Download references

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (61503222, 61673227, 61573008), in part by NSERC, Canada, in part by the Research Fund for the Taishan Scholar Project of Shandong Province of China, in part by the Chinese Postdoctoral Science Foundation (2016M602166), in part by the Fund for Postdoctoral Applied Research Projects of Qingdao (2016116), and in part by the Research Award Funds for Outstanding Young Scientists of Shandong Province (BS2014SF005).

Author information

Authors and Affiliations

  1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China

    Ziye Zhang & Shaowei Zhou

  2. Department of Electrical Engineering, Lakehead University, Thunder Bay, ON, P7B 5E1, Canada

    Ziye Zhang & Xiaoping Liu

  3. School of Information and Electrical Engineering, Shandong Jianzhu University, Jinan, 250101, China

    Xiaoping Liu

  4. Institute of Complexity Science, Qingdao University, Qingdao, 266071, China

    Chong Lin

Authors
  1. Ziye Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaoping Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chong Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shaowei Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiaoping Liu.

Ethics declarations

Conflict of interest

The authors declare that there are no conflict interests regarding the publication of this paper.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, Z., Liu, X., Lin, C. et al. Exponential stability analysis for delayed complex-valued memristor-based recurrent neural networks. Neural Comput & Applic 31, 1893–1903 (2019). https://doi.org/10.1007/s00521-017-3166-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-017-3166-6

Keywords

Search

Navigation