Skip to main content
SpringerLink
Log in

Adaptive Synchronization Control and Parameters Identification for Chaotic Fractional Neural Networks with Time-Varying Delays

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

In this paper, the adaptive synchronization control and synchronization-based parameters identification method for time-varying delayed fractional chaotic neural networks are proposed. Based on the adaptive control with suitable update law and linear feedback control, an analytical, rigorous, and simple adaptive control method is given, which can make two coupled fractional-order delayed neural networks achieve synchronization. In addition, the uncertain system parameters can also be identified along with the realization of synchronization. The speed of synchronization and parameter identification can be adjusted by selecting appropriate control parameters. Besides, the proposed method is very easy to accomplish in reality and has strong robustness against external disturbances. Finally, the numerical simulations are put into practice to illustrate the rationality and validity of theoretical analysis.

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

Similar content being viewed by others

References

  1. Diethelm K (2010) The analysis of fractional differential equations. Springer, Berlin

    Book  Google Scholar 

  2. Hu T, Zhang X et al (2018) Global asymptotic synchronization of nonidentical fractional-order neural networks. Neurocomputing 313:39–46

    Article  Google Scholar 

  3. Huang CD, Liu H et al (2020) Bifurcations in a fractional-order neural network with multiple leakage delays. Neural Netw 131:115–126

    Article  Google Scholar 

  4. Huang CD, Nie X et al (2019) Novel bifurcation results for a delayed fractional-order quaternion-valued neural network. Neural Netw 117:67–93

    Article  Google Scholar 

  5. Huang CD, Zhao X et al (2019) Disparate delays-induced bifurcations in a fractional-order neural network. J Frankl Inst 365:2825–2846

    Article  MathSciNet  Google Scholar 

  6. Huang CD, Li H et al (2019) Stability and bifurcation control in a fractional predator–prey model via extended delay feedback. Int J Bifurc Chaos 29:1950150

    Article  MathSciNet  Google Scholar 

  7. Huang CD, Cao J (2020) Bifurcation mechanisation of a fractional-order neural network with unequal delays. Neural Process Lett. https://doi.org/10.1007/s11063-020-10293-w

    Article  Google Scholar 

  8. Huang C, Lu J et al (2020) Stabilization of probabilistic Boolean networks via pinning control strategy. Inf Sci 510:205–217

    Article  MathSciNet  Google Scholar 

  9. Huang C, Lu J et al (2020) Stability and stabilization in probability of probabilistic Boolean networks. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2020.2978345

    Article  Google Scholar 

  10. Huang C, Zhang X et al (2020) Stabilization of probabilistic Boolean networks via pinning control strategy. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2020.2974143

    Article  Google Scholar 

  11. Hu J, Han Y et al (2010) Synchronizing chaotic systems using control based on a special matrix structure and extending to fractional chaotic systems. Commun Nonlinear Sci Numer Simul 15:115–123

    Article  MathSciNet  Google Scholar 

  12. Peng G (2007) Synchronization of fractional order chaotic systems. Phys Lett A 363:426–432

    Article  MathSciNet  Google Scholar 

  13. Pan L, Zhou W et al (2010) Synchronization and anti-synchronization of new uncertain fractional-order modified unified chaotic systems. Commun Nonlinear Sci Numer Simul 15:3754–3762

    Article  MathSciNet  Google Scholar 

  14. Lu J (2006) Nonlinear observer design to synchronize fractional-order chaotic systems via a scalar transmitted signal. Phys A 359:107–118

    Article  Google Scholar 

  15. Yang X, Li C et al (2018) Synchronization of fractional-order memristor-based complex-valued neural networks with uncertain parameters and time delays. Chaos Solitons Fract 110:105–123

    Article  MathSciNet  Google Scholar 

  16. Ding Z, Shen Y (2016) Projective synchronization of nonidentical fractional-order neural networks based on sliding mode controller. Neurocomputing 76:97–105

    MATH  Google Scholar 

  17. Wu H, Wang L et al (2017) Global projective synchronization in finite time of nonidentical fractional-order neural networks based on sliding mode control strategy. Neurocomputing 235:264–273

    Article  Google Scholar 

  18. Liao C, Lu C (2011) Design of delay-dependent state estimator for discrete-time recurrent neural networks with interval discrete and infinite-distributed time-varying delays. Cognit Neurodyn 5:133–143

    Article  Google Scholar 

  19. Yang X, Li C et al (2017) Quasi-uniform synchronization of fractional-order memristor-based neural networks with delay. Neurocomputing 234:205–215

    Article  Google Scholar 

  20. Chen J, Li C et al (2018) Global Mittag–Leffler projective synchronization of nonidentical fractional-order neural networks with delay via sliding mode control. Neurocomputing 313:324–332

    Article  Google Scholar 

  21. Zhang L, Yang Y et al (2018) Synchronization analysis of fractional-order neural networks with time-varying delays via discontinuous neuron activations. Neurocomputing 275:40–49

    Article  Google Scholar 

  22. Gu Y, Wang H et al (2019) Stability and synchronization for Riemann–Liouville fractional-order time-delayed inertial neural networks. Neurocomputing 340:270–280

    Article  Google Scholar 

  23. Parlitz U (1996) Estimating model parameters from time series by auto synchronization. Phys Rev Lett 76:1232–1236

    Article  Google Scholar 

  24. Zhao H, Li L et al (2016) Impulsive control for synchronization and parameters identification of uncertain multi-links complex network. Nonlinear Dyn 83:1437–1451

    Article  MathSciNet  Google Scholar 

  25. Zhao H, Li L et al (2017) Parameters tracking identification based on finite-time synchronization for multi-links complex network via periodically switch control. Chaos Solitons Fract 104:268–281

    Article  MathSciNet  Google Scholar 

  26. Ren H, Tian K et al (2018) Local time-varying topology identification of network with unknown parameters based on adaptive synchronization. Automatika 59:391–399

    Article  Google Scholar 

  27. Wang X, Gu H et al (2019) Identifying topologies and system parameters of uncertain time-varying delayed complex networks. Sci China Technol Sci 62:94–105

    Article  Google Scholar 

  28. He W, Cao J (2008) Adaptive synchronization of a class of chaotic neural networks with known or unknown parameters. Phys Lett A 372:408–416

    Article  Google Scholar 

  29. Liu C, Wang F (2020) Parameter identification of genetic regulatory network with time-varying delays via adaptive synchronization method. Adv Differ Equ 2020:127

    Article  MathSciNet  Google Scholar 

  30. Li H, Cao J et al (2019) Finite-time synchronization and parameter identification of uncertain fractional-order complex networks. Physica A 533:122027

    Article  MathSciNet  Google Scholar 

  31. Gu Y, Yu Y et al (2017) Synchronization-based parameter estimation of fractional-order neural networks. Physica A 483:351–361

    Article  MathSciNet  Google Scholar 

  32. Gu Y, Wang H et al (2020) Synchronization for commensurate Riemann–Liouville fractional-order memristor-based neural networks with unknown parameters. J Frankl Inst 357:8870–8898

    Article  MathSciNet  Google Scholar 

  33. Hu W, Wen G et al (2019) Differential evolution-based parameter estimation and synchronization of heterogeneous uncertain nonlinear delayed fractional-order multi-agent systems with unknown leader. Nonlinear Dyn 97:1087–1105

    Article  Google Scholar 

  34. Ma W, Li C et al (2014) Adaptive synchronization of fractional neural networks with unknown parameters and time delays. Entropy 16:6286–6299

    Article  MathSciNet  Google Scholar 

  35. Hua C, Wang Y et al (2019) Stability analysis of neural networks with time-varying delay using a new augmented Lyapunov–Krasovskii functional. Neurocomputing 332:1–9

    Article  Google Scholar 

  36. Li L, Sun Y (2015) Adaptive fuzzy control for nonlinear fractional-order uncertain systems with unknown uncertainties and external disturbance. Entropy 17:5580–5592

    Article  Google Scholar 

  37. Li H, Cao J et al (2018) Finite-time synchronization of fractional-order complex networks via hybrid feedback control. Neurocomputing 320:69–75

    Article  Google Scholar 

  38. Li C, Deng W (2007) Remarks on fractional derivatives. Appl Math Comput 187:777–784

    MathSciNet  MATH  Google Scholar 

  39. Andrilli S, Hecker D (2010) Elementary linear algebra, 4th edn. Academic Press, Burlington

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Finance and Mathematics, Huainan Normal University, 238 Dongshan West Road, Huainan, 232038, People’s Republic of China

    Yeguo Sun

  2. School of Computer Science, Huainan Normal University, 238 Dongshan West Road, Huainan, 232038, People’s Republic of China

    Yihong Liu

Authors
  1. Yeguo Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yihong Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yeguo Sun.

Ethics declarations

Conflict of interest

The authors declares 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 partly supported by the Natural Science Foundation of Anhui Province under Grant No. 2008085MF200, the University Natural Science Foundation of Anhui Province under Grant No. KJ2019ZD48, and the National Natural Science Foundation of China under Grant No. 61403157.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sun, Y., Liu, Y. Adaptive Synchronization Control and Parameters Identification for Chaotic Fractional Neural Networks with Time-Varying Delays. Neural Process Lett 53, 2729–2745 (2021). https://doi.org/10.1007/s11063-021-10517-7

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-021-10517-7

Keywords

Search

Navigation