Finite-Time Synchronization of Complex-Valued Neural Networks with Multiple Time-Varying Delays and Infinite Distributed Delays

Abstract

This paper investigates finite-time synchronization of complexed-valued neural networks with multiple time-varying delays and infinite distributed delays. By separating the complex-valued neural networks into the real and the imaginary parts, the corresponding equivalent real-valued systems are obtained. Some sufficient conditions are derived for finite-time synchronization of the drive-response system based on the new Lyapunov–Krasovskii function and the new analysis techniques. Numerical examples demonstrate the effectiveness of the theoretical results.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4

References

  1. 1.

    Lee D (2006) Improvement of complex-valued Hopfield associative memory by using generalized projection rules. IEEE Trans Neural Netw 17(5):1341–1347

    Article  Google Scholar 

  2. 2.

    Zhou W, Zurada J (2009) Discrete-time recurrent neural networks with complex-valued linear threshold neurons. IEEE Trans Circuits Syst II 56(8):669–673

    Article  Google Scholar 

  3. 3.

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

    Article  Google Scholar 

  4. 4.

    Dini D, Mandic D (2012) Class of widely linear complex Kalman filters. IEEE Trans Neural Netw Learn Syst 23(5):775–786

    Article  Google Scholar 

  5. 5.

    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 

  6. 6.

    Xu X, Zhang J, Shi J (2014) Exponential stability of complex-valued neural networks with mixed delays. Neurocomputing 128(128):483–490

    Article  Google Scholar 

  7. 7.

    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

    MathSciNet  Article  Google Scholar 

  8. 8.

    Pecora L, Carroll T (1990) Synchronization in chaotic systems. Phys Rev Lett 64(8):821–824

    MathSciNet  Article  Google Scholar 

  9. 9.

    Aihara K, Takabe T, Toyoda M (1990) Chaotic neural networks. Phys Lett A 144(6):333–340

    MathSciNet  Article  Google Scholar 

  10. 10.

    Tan Z, Ali M (2001) Associative memory using synchronization in a chaotic neural network. Int J Mod Phys C 12(1):19–29

    Article  Google Scholar 

  11. 11.

    Hoppensteadt F, Izhikevich E (2002) Pattern recognition via synchronization in phase-locked loop neural networks. IEEE Trans Neural Netw 11(3):734–738

    Article  Google Scholar 

  12. 12.

    Park H (2006) Chaos synchronization between two different chaotic dynamical systems. Chaos Solitons Fractals 27(2):549–554

    Article  Google Scholar 

  13. 13.

    Bowong S, Kakmeni F, Fotsin H (2006) A new adaptive observer-based synchronization scheme for private communication. Phys Lett A 355(3):193–201

    Article  Google Scholar 

  14. 14.

    Sheng L, Yang H (2008) Exponential synchronization of a class of neural networks with mixed time-varying delays and impulsive effects. Neurocomputing 71(16):3666–3674

    Article  Google Scholar 

  15. 15.

    Song Q (2009) Design of controller on synchronization of chaotic neural networks with mixed time-varying delays. Neurocomputing 72(13):3288–3295

    Article  Google Scholar 

  16. 16.

    Wang Z, Zhang H (2013) Synchronization stability in complex interconnected neural networks with nonsymmetric coupling. Neurocomputing 108(5):84–92

    Article  Google Scholar 

  17. 17.

    Shen J, Cao J (2011) Finite-time synchronization of coupled neural networks via discontinuous controllers. Cogn Neurodyn 5(4):373–385

    Article  Google Scholar 

  18. 18.

    Yang X, Cao J (2010) Finite-time stochastic synchronization of complex networks. Appl Math Model 34(11):3631–3641

    MathSciNet  Article  Google Scholar 

  19. 19.

    Mei J, Jiang M, Wang X, Han J, Wang S (2014) Finite-time synchronization of drive-response systems via periodically intermittent adaptive control. J Frankl Inst 351(5):2691–2710

    MathSciNet  Article  Google Scholar 

  20. 20.

    Fei Y, Mei J, Wu Z (2016) Finite-time synchronisation of neural networks with discrete and distributed delays via periodically intermittent memory feedback control. IET Control Theory Appl 10(10):1630–1640

    MathSciNet  Google Scholar 

  21. 21.

    Huang J, Li C, Huang T, He X (2014) Finite-time lag synchronization of delayed neural networks. Neurocomputing 139(13):145–149

    Article  Google Scholar 

  22. 22.

    Hu C, Yu J, Jiang H (2014) Finite-time synchronization of delayed neural networks with Cohen–Grossberg type based on delayed feedback control. Neurocomputing 143(16):90–96

    Article  Google Scholar 

  23. 23.

    Shen H, Park J, Wu Z, Zhang Z (2015) Finite-time \(H^{\infty }\) synchronization for complex networks with semi-Markov jump topology. Commun Nonlinear Sci Numer Simul 24(1–3):40–51

    MathSciNet  Article  Google Scholar 

  24. 24.

    Shen H, Ju H, Wu Z (2014) Finite-time synchronization control for uncertain Markov jump neural networks with input constraints. Nonlinear Dyn 77(4):1709–1720

    MathSciNet  Article  Google Scholar 

  25. 25.

    Yang X (2014) Can neural network swith arbitrary delays be finite-timely synchronized. Neurocomputing 143(16):275–281

    Article  Google Scholar 

  26. 26.

    Shi L, Yang X, Li Y, Feng Z (2016) Finite-time synchronization of nonidentical chaotic systems with multiple time-varying delays and bounded perturbations. Nonlinear Dyn 83(1):75–87

    MathSciNet  Article  Google Scholar 

  27. 27.

    Zhou C, Zhang W, Yang X, Xu C, Feng J (2017) Finite-time synchronization of complex-valued neural networks with mixed delays and uncertain perturbations. Neural Process Lett 1(4):1–21

    Google Scholar 

Download references

Acknowledgements

This work was partially supported by the National Natural Science Foundation of China (Grant No. 61403050), the science and technology commission project of Chongqing (cstc2017jcyjA1082, cstc2018jcyjAX0810), the Scientific and Technological Research Program of Chongqing Municipal Education Commission (KJ1501412, KJ1601401, KJ1601410), and the Foundation of CQUE (KY201702A,KY201720B).

Author information

Affiliations

Authors

Corresponding author

Correspondence to Junjian Huang.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Liu, Y., Qin, Y., Huang, J. et al. Finite-Time Synchronization of Complex-Valued Neural Networks with Multiple Time-Varying Delays and Infinite Distributed Delays. Neural Process Lett 50, 1773–1787 (2019). https://doi.org/10.1007/s11063-018-9958-6

Download citation

Keywords

  • Finite-time synchronization
  • Complexed-valued neural networks
  • Multiple time-varying delays
  • Infinite distributed delays
  • Lyapunov–Krasovskii function