SpringerLink
Log in

Exploring the Impact of Delay on Hopf Bifurcation of a Type of BAM Neural Network Models Concerning Three Nonidentical Delays

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

In this research, a kind of BAM neural networks containing three nonidentical time delays are explored. Exploiting fixed point knowledge, we examine that the solution to the concerned BAM neural network models exists and is unique. Exploiting a apposite function, we check that the solution to the concerned BAM neural network models is bounded. In line with different delay cases, we systematically analyze the characteristic equations of the concerned BAM neural network models. A set of innovative bifurcation criteria of the concerned BAM neural network models under the six delay situations are acquired. The impact of delay is adequately revealed under different delay cases. The research indicates that delay plays a pivotal role in dominating stability domain and the time that Hopf bifurcation arises. of the concerned BAM neural networks. In order to sustain the theoretical assertions, we present the corresponding software simulation plots. The acquired conclusion of this research are completely novel and has momentous theoretical values in dominating and devising networks.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

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
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30

Similar content being viewed by others

Data Availibility Statement

No data were used to support this study.

References

  1. Dong T, Liao XF (2013) Hopf–Pitchfork bifurcation in a simplified BAM neural network model with multiple delays. J Comput Appl Math 253:222–234

    Article  MathSciNet  MATH  Google Scholar 

  2. Song YL, Han MA, Wei JJ (2005) Stability and Hopf bifurcation analysis on a simplified BAM neural network with delays. Physica D 200:185–204

    Article  MathSciNet  MATH  Google Scholar 

  3. Ge JH, Xu J (2016) Stability switches and bifurcation analysis in a coupled neural system with multiple delays. Sci China Technol Sci 59:920–931

    Article  Google Scholar 

  4. Mohamed Thoiyab N, Muruganantham P, Zhu QX, Gunasekaran N (2021) Novel results on global stability analysis for multiple time-delayed BAM neural networks under parameter uncertainties. Chaos, Solitons Fractals 152:111441

    Article  MathSciNet  MATH  Google Scholar 

  5. Wang SZ, Zhang ZY, Lin C, Chen J (2021) Fixed-time synchronization for complex-valued BAM neural networks with time-varying delays via pinning control and adaptive pinning control. Chaos, Solitons Fractals 153:111583

    Article  MathSciNet  MATH  Google Scholar 

  6. Gan YT, Liu C, Peng H, Liu F, Rao HX (2020) Anti-synchronization for periodic BAM neural networks with Markov scheduling protocol. Neurocomputing 417:585–592

    Article  Google Scholar 

  7. Xu CJ, Liu ZX, Liao MX, Li PL, **ao QM, Shuai Y (2021) Fractional-order bidirectional associate memory (BAM) neural networks with multiple delays: The case of Hopf bifurcation. Math Comput Simul 182:471–494

    Article  MathSciNet  MATH  Google Scholar 

  8. Syed Ali M, Narayanan G, Shekher V, Alsaedi A, Ahmad B (2020) Global Mittag-Leffler stability analysis of impulsive fractional-order complex-valued BAM neural networks with time varying delays. Commun Nonlinear Sci Numer Simul 83:105088

    Article  MathSciNet  MATH  Google Scholar 

  9. Ayachi M (2022) Measure-pseudo almost periodic dynamical behaviors for BAM neural networks with D operator and hybrid time-varying delays. Neurocomputing 486:160–173

    Article  Google Scholar 

  10. Li YK, **ang JL (2019) Existence and global exponential stability of anti-periodic solution for Clifford-valued inertial CohenCGrossberg neural networks with delays. Neurocomputing 332:259–269

    Article  Google Scholar 

  11. Xu CJ, Zhang W, Aouiti C, Liu ZX, Liao MX, Li PL (2023) Further investigation on bifurcation and their control of fractional-order BAM neural networks involving four neurons and multiple delays. Math Methods Appl Sci 46(3):3091–3114

    Article  MathSciNet  Google Scholar 

  12. Xu CJ, Liao MX, Li PL, Guo Y, Liu ZX (2021) Bifurcation properties for fractional order delayed BAM neural networks. Cogn Comput 13(2):322–356

    Article  Google Scholar 

  13. Xu CJ, Li PL, Pang YC (2016) Exponential stability of almost periodic solutions for memristor-based neural networks with distributed leakage delays. Neural Comput 28(12):2726–2756

    Article  MathSciNet  MATH  Google Scholar 

  14. Xu CJ, Zhang QM (2014) On anti-periodic solutions for Cohen-Grossberg shunting inhibitory neural networks with time-varying delays and impulses. Neural Comput 26(10):2328–2349

    Article  MathSciNet  MATH  Google Scholar 

  15. Arslan E, Narayanan G, Ali MS, Arik S, Saroha S (2020) Controller design for finite-time and fixed-time stabilization of fractional-order memristive complex-valued BAM neural networks with uncertain parameters and time-varying delays. Neural Netw 130:60–74

    Article  MATH  Google Scholar 

  16. **ao M, Zheng WX, Jiang GP, Cao JD (2021) Qualitative analysis and bifurcation in a neuron system with memristor characteristics and time delay. IEEE Trans Neural Netw Learn Syst 32(5):1974–1988

    Article  MathSciNet  Google Scholar 

  17. Yan YP (2006) Hopf bifurcation and stability for a delayed tri-neuron network model. J Comput Appl Math 196:579–595

    Article  MathSciNet  MATH  Google Scholar 

  18. Yan YP (2008) Bifurcation analysis in a simplified tri-neuron BAM network model with multiple delays. Nonlinear Anal Real World Appl 9:963–976

    Article  MathSciNet  MATH  Google Scholar 

  19. Xu CJ, Tang XH, Liao MX (2010) Frequency domain analysis for bifurcation in a simplified tri-neuron BAM network model with two delays. Neural Netw 23(7):872–880

    Article  MATH  Google Scholar 

  20. Xu CJ, Liao MX, Li PL, Yuan S (2021) Impact of leakage delay on bifurcation in fractional-order complex-valued neural networks. Chaos, Solitons Fractals 142:110535

    Article  MathSciNet  MATH  Google Scholar 

  21. Xu CJ, Zhang W, Liu ZX, Yao LY (2022) Delay-induced periodic oscillation for fractional-order neural networks with mixed delays. Neurocomputing 488:681–693

    Article  Google Scholar 

  22. Xu CJ, Zhang W, Liu ZX, Li PL, Yao LY (2022) Bifurcation study for fractional-order three-layer neural networks involving four time delays. Cogn Comput 16:1233–1248

    Google Scholar 

  23. Huang CD, Wang J, Chen XP, Cao JD (2021) Bifurcations in a fractional-order BAM neural network with four different delays. Neural Netw 141:344–354

    Article  MATH  Google Scholar 

  24. Huang CD, Liu H, Shi XY, Chen XP, **ao M, Wang ZX, Cao JD (2020) Bifurcations in a fractional-order neural network with multiple leakage delays. Neural Netw 131:115–126

    Article  MATH  Google Scholar 

  25. Huang CD, Cao JD, **ao M, Alsaedi A, Hayat T (2018) Effects of time delays on stability and Hopf bifurcation in a fractional ring-structured network with arbitrary neurons. Commun Nonlinear Sci Numer Simul 57:1–13

    Article  MathSciNet  MATH  Google Scholar 

  26. Amine S, Hajri Y, Allali K (2022) A delayed fractional-order tumor virotherapy model: Stability and Hopf bifurcation. Chaos, Solitons Fractals 161:112396

    Article  MathSciNet  MATH  Google Scholar 

  27. Shi JP, He K, Fang H (2022) Chaos, Hopf bifurcation and control of a fractional-order delay financial system. Math Comput Simul 194:348–364

    Article  MathSciNet  MATH  Google Scholar 

  28. Mu D, Xu CJ, Liu ZX, Pang YC (2023) Further insight into bifurcation and hybrid control tactics of a chlorine dioxide-iodine-malonic acid chemical reaction model incorporating delays. MATCH Commun Math Comput Chem 89(3):529–566

    Article  MATH  Google Scholar 

  29. Xu CJ, Cui XH, Li PL, Yan JL, Yao LY (2023) Exploration on dynamics in a discrete predator-prey competitive model involving time delays and feedback controls. J Biol Dyn 17(1):2220349

    Article  MATH  Google Scholar 

  30. Xu CJ, Mu D, Liu ZX, Pang YC, Liao MX, Aouiti C (2023) New insight into bifurcation of fractional-order 4D neural networks incorporating two different time delays. Commun Nonlinear Sci Numer Simul 118:107043

    Article  MathSciNet  MATH  Google Scholar 

  31. Ou W, Xu CJ, Cui QY, Liu ZX, Pang YC, Farman M, Ahmad S, Zeb A (2023) Mathematical study on bifurcation dynamics and control mechanism of tri-neuron BAM neural networks including delay. Math Methods Appl Sci. https://doi.org/10.1002/mma.9347

    Article  Google Scholar 

  32. Li PL, Lu YJ, Xu CJ, Ren J (2023) Insight into Hopf bifurcation and control methods in fractional order BAM neural networks incorporating symmetric structure and delay. Cogn Comput. https://doi.org/10.1007/s12559-023-10155-2

    Article  Google Scholar 

  33. Li HL, Zhang L, Hu C, Jiang YL, Teng ZD (2017) Dynamical analysis of a fractional-order prey-predator model incorporating a prey refuge. J Appl Math Comput 54:435–449

    Article  MathSciNet  MATH  Google Scholar 

  34. Sun QS, **ao M, Tao BB (2018) Local bifurcation analysis of a fractional-order dynamic model of genetic regulatory networks with delays. Neural Process Lett 47(3):1285–1296

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, 471023, People’s Republic of China

    Peiluan Li, Rong Gao & Ying Li

  2. Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang, 550004, People’s Republic of China

    Chang** Xu

  3. Guizhou Key Laboratory of Big Data Statistical Analysis, Guiyang, 550025, People’s Republic of China

    Chang** Xu

  4. School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou, 450046, People’s Republic of China

    Jianwei Shen

  5. Department of Mathematics, University of Malakand, Chakdara, Dir Lower, Khyber Pakhtunkhwa, Pakistan

    Shabir Ahmad

Authors
  1. Peiluan Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rong Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chang** Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jianwei Shen
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Shabir Ahmad
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Ying Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chang** Xu.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

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

The work is supported by National Natural Science Foundation of China Nos. 12261015 and No.62062018), Project of High-level Innovative Talents of Guizhou Province ([2016]5651), Guizhou Key Laboratory of Big Data Statistical Analysis( No. [2019]5103), University Science and Technology Top Talents Project of Guizhou Province (KY[2018]047), Foundation of Science and Technology of Guizhou Province ([2019]1051).

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, P., Gao, R., Xu, C. et al. Exploring the Impact of Delay on Hopf Bifurcation of a Type of BAM Neural Network Models Concerning Three Nonidentical Delays. Neural Process Lett 55, 11595–11635 (2023). https://doi.org/10.1007/s11063-023-11392-0

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-023-11392-0

Keywords

Search

Navigation