Skip to main content
SpringerLink
Log in

Finite-Time Synchronization of Coupled Inertial Memristive Neural Networks with Mixed Delays via Nonlinear Feedback Control

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

The finite-time synchronization of coupled inertial memristive neural networks (IMNNs) systems is discussed in this paper. Firstly, a mathematical model of IMNNs with time-varying delays is given, then the original system is transformed into a first-order differential equation by selecting a suitable variable substitution. Secondly, by using two different controllers and the definition of the upper right-hand derivative, it can be guaranteed that finite-time and fixed-time synchronization between response system and drive system based on finite time stability and fixed time theory. Finally, two numerical simulations are given to illustrate the effectiveness of the main 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
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

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

    Google Scholar 

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

    Google Scholar 

  3. Baoa H, Cao J (2015) Projective synchronization of fractional-order memristor-based neural networks. Neural Netw 63:1–9

    Google Scholar 

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

    MATH  Google Scholar 

  5. Wen S, Zeng Z, Huang T (2012) Exponential stability analysis of memristor-based recurrent neural networks with time-varying delays. Neurocomputing 97:233–240

    Google Scholar 

  6. Xiong Z, Yin H, Liang M et al (2017) Stability analysis for stochastic neutral-type memristive neural networks with time-varying delay and s-type distributed delays. Math Probl Eng. https://doi.org/10.1155/2017/3273758

    Article  MathSciNet  MATH  Google Scholar 

  7. Yang X, Cao J, Qiu J (2015) Pth moment exponential stochastic synchronization of coupled memristor-based neural networks with mixed delays via delayed impulsive control. Neural Netw 65:80–91

    MATH  Google Scholar 

  8. Fu Q, Cai J, Zhong S et al (2017) Dissipativity and passivity analysis for memristor-based neural networks with leakage and two additive time-varying delays. Neurocomputing. https://doi.org/10.1016/j.neucom.2017.09.014

    Article  Google Scholar 

  9. Yang C, Xiong Z, Hong D (2018) Analysis of adaptive synchronization for stochastic neutral-type memristive neural networks with mixed time-varying delays. Discrete Dyn Nat Soc. https://doi.org/10.1155/2018/8126127

    Article  MathSciNet  MATH  Google Scholar 

  10. Li N, Cao J (2018) Synchronization criteria for multiple memristor-based neural networks with time delay and inertial term. Sci China Technol Sci 61:612–622

    Google Scholar 

  11. Babcock K, Westervelt R (1987) Stability and dynamics of simple electronic neural networks with added inertia. Phys D Nonlinear Phenom 23:464–469

    Google Scholar 

  12. Zhang G, Zeng Z, Hu J (2018) New results on global exponential dissipativity analysis of memristive inertial neural networks with distributed time-varying delays. Neural Netw 97:183–191

    Google Scholar 

  13. Feng Y, Xiong X, Tang R et al (2018) Exponential synchronization of inertial neural networks with mixed delays via quantized pinning control. Neurocomputing 310:165–171

    Google Scholar 

  14. Wang Z, Huang X, Shi G (2011) Analysis of nonlinear dynamics and chaos in a fractional order financial system with time delay. Comput Math Appl 62:1531–1539

    MathSciNet  MATH  Google Scholar 

  15. Zhou J, Sang C, Li X et al (2018) \(H_{\infty }\) consensus for nonlinear stochastic multi-agent systems with time delay. Appl Math Comput 325:41–58

    MathSciNet  MATH  Google Scholar 

  16. Yang X, Cao J, Liang J (2017) Exponential synchronization of memristive neural networks with delays: interval matrix method. IEEE Trans Cybern 28:1878–1888

    MathSciNet  Google Scholar 

  17. Zhang H, Ye M, Cao J et al (2018) Synchronization stability of Riemann–Liouville fractional delay-coupled complex neural networks. Physica A 508:115–165

    MathSciNet  Google Scholar 

  18. Zhang W, Zhang H, Cao J et al (2019) Synchronization in uncertain fractional-order memristive complex-valued neural networks with multiple time delays. Neural Netw 110:186–198

    Google Scholar 

  19. Jiang M, Wang S, Mei J et al (2012) Synchronization control of a class of memristor-based recurrent neural networks. Inf Sci 183:106–116

    MathSciNet  Google Scholar 

  20. Scholtes I, Botev J, Esch M et al (2009) Epidemic self-synchronization in complex networks. Int Conf Complex Sci 5:1794–1809

    MATH  Google Scholar 

  21. Zheng M, Li L, Peng H et al (2018) Globally fixed-time synchronization of coupled neutral-type neural network with mixed time-varying delays. Plos ONE. https://doi.org/10.1371/journal.pone.0191473

    Article  Google Scholar 

  22. Abdurahman A, Jiang H, Teng Z (2015) Finite-time synchronization for fuzzy cellular neural networks with time-varying delays. Fuzzy Sets Syst 297:96–111

    MathSciNet  MATH  Google Scholar 

  23. Ji G, Hu C, Yu J et al (2018) Finite-time and fixed-time synchronization of discontinuous complex networks: a unified control framework design. J Frankl Inst 355:4665–4685

    MathSciNet  MATH  Google Scholar 

  24. Zhang W, Yang X, Xu C et al (2018) Finite-time synchronization of discontinuous neural networks nith delays and mismatched parameters. IEEE Trans Neural Netw Learn Syst 29:3761–3771

    MathSciNet  Google Scholar 

  25. Xu C, Yang X, Lu J et al (2018) Finite-time synchronization of networks via quantized intermittent pinning control. IEEE Trans Cybern 48:3021–3027

    Google Scholar 

  26. Chen C, Li L, Peng H et al (2017) Finite-time synchronization of memristor-based neural networks with mixed delays. Neurocomputing 235:83–89

    Google Scholar 

  27. Cao J, Li R, Mathematics S (2017) Fixed-time synchronization of delayed memristor-based recurrent neural networks. Sci China Inform Sci 60:032201

    Google Scholar 

  28. Xiong X, Tang R, Yang X (2018) Finite-time synchronization of memristive neural networks with proportional delay. Neural Process Lett. https://doi.org/10.1007/s11063-018-9910-9

    Article  Google Scholar 

  29. Zhou C, Zhang W, Yang X et al (2017) Finite-time synchronization of complex-valued neural networks with mixed delays and uncertain perturbations. Neural Process Lett 46:271–291

    Google Scholar 

  30. Yang X, Cao J, Xu C et al (2018) Finite-time stabilization of switched dynamical networks with quantized couplings via quantized controller. Sci China Technol Sci 61:299–308

    Google Scholar 

  31. Cao J, Li R, Mathematics S (2014) Finite-time synchronization of markovian jump complex networks with partially unknown transition rates. J Frankl Inst 351:2543–2561

    MathSciNet  Google Scholar 

  32. Liu M, Jiang H, Hu C (2017) Finite-time synchronization of delayed dynamical networks via aperiodically intermittent control. J Frankl Inst 354:5374–5397

    MathSciNet  MATH  Google Scholar 

  33. Yang X, Lam J, Ho D et al (2017) Fixed-time synchronization of complex networks with impulsive effects via non-chattering control. IEEE Trans Autom Control 62:5511–5521

    MATH  Google Scholar 

  34. Mei J, Jiang M, Xu W et al (2013) Finite-time synchronization control of complex dynamical networks with time delay. Commun Nonlinear Sci Numer Simul 18:2462–2478

    MathSciNet  MATH  Google Scholar 

  35. Liu X, Su H, Chen M (2016) A switching approach to designing finite-time synchronization controllers of coupled neural networks. IEEE Trans Neural Netw Learn Syst 27:471–482

    MathSciNet  Google Scholar 

  36. Zhu X, Yang X, Alsaadi F et al (2018) Fixed-time synchronization of coupled discontinuous neural networks with nonidentical perturbations. Neural Process Lett 48:1161–1174

    Google Scholar 

  37. Feng Y, Yang X, Cao J et al (2018) Synchronization of memristive neural networks with mixed delays via quantized intermittent control. Appl Math Comput 339:874–887

    MathSciNet  MATH  Google Scholar 

  38. Tavazoei M, Haeri M (2008) Synchronization of chaotic fractional-order systems via active sliding mode controller. Physica A 387:57–70

    Google Scholar 

  39. Yang T, Chua L (1997) Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication. IEEE Trans Circuits Syst I Fundam Theory Appl 44:976–988

    MathSciNet  Google Scholar 

  40. Franklin G, Emami-Naeini A, Powell J (1993) Feedback control of dynamic systems. IEEE Trans Circuit Theory 1:157–175

    MATH  Google Scholar 

  41. Ye R, Liu X, Zhang H et al (2019) Global mittag-leffler synchronization for fractional-order BAM neural networks with impulses and multiple variable delays via delayed-feedback control strategy. Neural Process Lett 49:1–18

    Google Scholar 

  42. Bernfeld S (1990) Differential equations with discontinuous righthand sides (A. F. Filippov). SIAM Rev 32:312–315

    Google Scholar 

  43. Ledyaev Y, Clarke F, Wolenski P et al (1998) Nonsmooth analysis and control theory. Springer, Berlin

    MATH  Google Scholar 

  44. Aubin J, Cellina A (1984) Differential inclusions. Springer, Berlin

    MATH  Google Scholar 

  45. Huang D, Jiang M, Jian J (2017) Finite-time synchronization of inertial memristive neural networks with time-varying delays via sampled-date control. Neurocomputing 266:527–539

    Google Scholar 

  46. Guo Z, Gong S, Huang T (2018) Finite-time synchronization of inertial memristive neural networks with time delay via delay-dependent control. Neurocomputing 293:100–107

    Google Scholar 

  47. Rakkiyappan R, Gayathri D, Velmurugan G et al (2019) Exponential synchronization of inertial memristor-based neural networks with time delay using average impulsive interval approach. Neural Process Lett. https://doi.org/10.1007/s11063-019-09982-y

    Article  Google Scholar 

Download references

Acknowledgements

The authors thank National Natural Science Foundation of China (No. 61563033) for its financial support.

Author information

Authors and Affiliations

  1. Department of Mathematics, Nanchang University, Nanchang, 330031, Jiangxi Province, People’s Republic of China

    Cuiping Yang, Zuoliang Xiong & Tianqing Yang

Authors
  1. Cuiping Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zuoliang Xiong
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tianqing Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zuoliang Xiong.

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

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, C., Xiong, Z. & Yang, T. Finite-Time Synchronization of Coupled Inertial Memristive Neural Networks with Mixed Delays via Nonlinear Feedback Control. Neural Process Lett 51, 1921–1938 (2020). https://doi.org/10.1007/s11063-019-10180-z

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-019-10180-z

Keywords

Search

Navigation