Skip to main content
SpringerLink
Log in

Robust Asymptotic Stability and Projective Synchronization of Time-Varying Delayed Fractional Neural Networks Under Parametric Uncertainty

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

In this paper, the robust asymptotic stability and projective synchronization of fractional-order time-varying delayed neural networks with uncertain parameters are studied. On account of the homeomorphism mapping theorem, free-weighting method and generalized Halanay inequality, several sufficient conditions of existence, uniqueness and asymptotic stability of the equilibrium point of the addressed models in the form of LMIs are established. In addition, some criteria ensuring the robust asymptotic projective synchronization between the master system and the slave system are deduced based on a suitable controller. Finally, two numerical simulations are designed to illustrate the effectiveness and rationality of the theoretical 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

Similar content being viewed by others

References

  1. Kulish VV, Lage JL (2002) Application of fractional calculus to fluid mechanics. J Fluids Eng 124(3):803–806

    Article  Google Scholar 

  2. Lundstrom BN, Higgs MH, Spain WJ, Fairhall AL (2008) Fractional differentiation by neocortical pyramidal neurons. Nat Neurosci 11:1335–1342

    Article  Google Scholar 

  3. Cao JD, Yuan K, Li HX (2006) Global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays. IEEE Trans Neural Netw 17(6):1646–1651

    Article  Google Scholar 

  4. Huang TW, Li CD, Duan SK, Starzyk JA (2012) Robust exponential stability of uncertain delayed neural networks with stochastic perturbation and impulse effects. IEEE Trans Neural Netw Learn Syst 23(6):866–875

    Article  Google Scholar 

  5. Tan GQ, Wang ZS, Shi Z (2021) Proportional-integral state estimator for quaternion-valued neural networks with time-varying delays. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2021.3103979

    Article  Google Scholar 

  6. Xiao SS, Wang ZS, Tian YF (2021) Stability analysis of delayed recurrent neural networks via a quadratic matrix convex combination approach. IEEE Trans Neural Netw Lear Syst. https://doi.org/10.1109/TNNLS.2021.3107427

    Article  Google Scholar 

  7. Podlubny I (1999) Fractional differential equations. Academic Press

  8. Sabatier J, Moze M, Farges C (2010) LMI stability conditions for fractional order systems. Comput Math Appl 59(5):1594–1609

    Article  MathSciNet  MATH  Google Scholar 

  9. Deng WH, Li CP, Lü JH (2007) Stability analysis of linear fractional differential system with multiple time delays. Nonlinear Dyn 48(4):409–416

    Article  MathSciNet  MATH  Google Scholar 

  10. Li Y, Chen YQ, Podlubny I (2009) Mittag-Leffler stability of fractional order nonlinear dynamic systems. Automatica 45(8):1965–1969

    Article  MathSciNet  MATH  Google Scholar 

  11. Wang H, Yu YG, Wen GG, Zhang S, Yu JZ (2015) Global stability analysis of fractional-order Hopfield neural networks with time delay. Neurocomputing 154:15–23

    Article  Google Scholar 

  12. Song QK, Chen YX, Zhao ZJ, Liu YR, Alsaadi FE (2021) Robust stability of fractional-order quaternion-valued neural networks with neutral delays and parameter uncertainties. Neurocomputing 420:70–81

    Article  Google Scholar 

  13. Kaslik E, Sivasundaram S (2012) Nonlinear dynamics and chaos in fractional-order neural networks. Neural Netw 32:245–256

    Article  MATH  Google Scholar 

  14. Chen LP, Huang TW (2019) Delay-dependent criterion for asymptotic stability of a class of fractional-order memristive neural networks with time-varying delays. Neural Netw 118:289–299

    Article  MATH  Google Scholar 

  15. Yang XJ, Song QK, Liu YR, Zhao ZJ (2015) Finite-time stability analysis of fractional-order neural networks with delay. Neurocomputing 152:19–26

    Article  Google Scholar 

  16. Chen JY, Li CD, Yang XJ (2018) Asymptotic stability of delayed fractional-order fuzzy neural networks with impulse effects. J Frankl Inst 355(15):7595–7608

    Article  MathSciNet  MATH  Google Scholar 

  17. Zhu H, He ZS, Zhou SB (2011) Lag synchronization of the fractional-order system via nonlinear observer. Int J Modern Phys B 25(29):3951–3964

    Article  MATH  Google Scholar 

  18. Erjaee GH, Momani S (2008) Phase synchronization in fractional differential chaotic systems. Phys Lett A 372(14):2350–2354

    Article  MATH  Google Scholar 

  19. Bao HB, Park JH, Cao JD (2015) Adaptive synchronization of fractional-order memristor-based neural networks with time delay. Nonlinear Dyn 82(3):1343–1354

    Article  MathSciNet  MATH  Google Scholar 

  20. Liu P, Kong MX, Zeng ZG (2020) Projective synchronization analysis of fractional-order neural networks with mixed time delays. IEEE Trans Cybern 1-11

  21. Yang XJ, Li CD, Song QK, Chen JY, Huang JJ (2018) Global Mittag-Leffler stability and synchronization analysis of fractional-order quaternion-valued neural networks with linear threshold neurons. Neural Netw 105:88–1033

    Article  MATH  Google Scholar 

  22. Xiao JY, Cao JD, Cheng J, Zhong SM, Wen SP (2020) Novel methods to finite-time Mittag-Leffler synchronization problem of fractional-order quaternion-valued neural networks. Inform Sci 526:221–244

    Article  MathSciNet  MATH  Google Scholar 

  23. Li HL, Hu C, Cao JD, Jiang HJ, Alsaedi A (2019) Quasi-projective and complete synchronization of fractional-order complex-valued neural networks with time delays. Neural Netw 118:102–109

    Article  MATH  Google Scholar 

  24. Wu A, Zeng ZG (2013) Anti-synchronization control of a class of memristive recurrent neural networks. Commun Nonlinear Sci Numer Simul 18(2):373–385

    Article  MathSciNet  MATH  Google Scholar 

  25. Zhang WW, Sha CL, Cao JD, Wang JL, Wang Y (2021) Adaptive quaternion projective synchronization of fractional order delayed neural networks in quaternion field. Appl Math Comput 400:126045

    MathSciNet  MATH  Google Scholar 

  26. Yang SA, Yu J, Hu C, Jiang HJ (2018) Quasi-projective synchronization of fractional-order complex-valued recurrent neural networks. Neural Netw 104:104–113

    Article  MATH  Google Scholar 

  27. Bao HB, Cao JD (2015) Projective synchronization of fractional-order memristor-based neural networks. Neural Netw 63:1–9

    Article  MATH  Google Scholar 

  28. Chen JY, Li CD, Yang XJ (2018) Global Mittag-Leffler projective synchronization of nonidentical fractional-order neural networks with delay via sliding mode control. Neurocomput 313:324–332

    Article  Google Scholar 

  29. Chen JR, Jiao LC, Wu JS, Wang XD (2010) Projective synchronization with different scale factors in a driven-response complex network and its application in image encryption. Nonlinear Anal: Real World Appl 11(4):3045–3058

    Article  MATH  Google Scholar 

  30. Wu XJ, Wang H, Lu HT (2011) Hyperchaotic secure communication via generalized function projective synchronization. Nonlinear Anal: Real World Appl 12(2):1288–1299

    Article  MathSciNet  MATH  Google Scholar 

  31. Li CD, Wu SC, Feng GG, Liao XF (2011) Stabilizing effects of impulses in discrete-time delayed neural networks. IEEE Trans Neural Netw 22(2):323–329

    Article  Google Scholar 

  32. Yang XJ, Li CD, Huang TW, Song QK, Huang JJ (2018) Synchronization of fractional-order memristor-based complex-valued neural networks with uncertain parameters and time delays. Chaos, Solitons & Fractals 110:105–123

    Article  MathSciNet  MATH  Google Scholar 

  33. Chen XF, Li ZS, Song QK, Hu J (2017) Robust stability analysis of quaternion-valued neural networks with time delays and parameter uncertainties. Neural Netw 91:55–65

    Article  MATH  Google Scholar 

  34. Huang WQ, Song QK, Zhao ZJ (2021) Robust stability for a class of fractional-order complex-valued projective neural networks with neutral-type delays and uncertain parameters. Neurocomputing 450(25):399–410

    Article  Google Scholar 

  35. Xie LH, Fu MY (1992) \(H_\infty \) control and quadratic stabilization of systems with parameter uncertainty via output feedback. IEEE Trans Auto Control 37(8):1253–1256

    Article  MathSciNet  MATH  Google Scholar 

  36. Liang S, Wu RC, Chen LP (2016) Adaptive pinning synchronization in fractional-order uncertain complex dynamical networks with delay. Phys A: Stat Mech Appl 444:49–62

    Article  MathSciNet  MATH  Google Scholar 

  37. Zhang JY (2003) Global stability analysis in Hopfield neural networks. Appl Math Lett 16(6):925–931

    Article  MathSciNet  MATH  Google Scholar 

  38. Diethelm K, Ford NJ (2002) Analysis of fractional differential equations. J Math Anal Appl 265(2):229–248

    Article  MathSciNet  MATH  Google Scholar 

  39. Diethelm K, Ford NJ, Freed AD (2002) A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dyn 29:3–22

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant 61906023, the Chongqing Research Program of Basic Research and Frontier Technology under Grant cstc2019jcyj-msxmX0710 and cstc2019jcyj-msxmX0722, and in part by the Science and Technology Research Program of Chongqing Municipal Education Commission (KJQN201900701), the Team Building Project for Graduate Tutors in Chongqing (JDDSTD201802), and the Group Building Scientific Innovation Project for universities in Chongqing (CXQT21021).

Author information

Authors and Affiliations

  1. Department of Mathematics, Chongqing Jiaotong University, Chongqing, 400074, China

    Mengqi Li, Xujun Yang, Qiankun Song & Xiaofeng Chen

Authors
  1. Mengqi Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xujun Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qiankun Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xiaofeng Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xujun Yang.

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

Li, M., Yang, X., Song, Q. et al. Robust Asymptotic Stability and Projective Synchronization of Time-Varying Delayed Fractional Neural Networks Under Parametric Uncertainty. Neural Process Lett 54, 4661–4680 (2022). https://doi.org/10.1007/s11063-022-10825-6

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-022-10825-6

Keywords

Search

Navigation