Skip to main content
SpringerLink
Log in

On Exponential Stability for Delayed Inertial BAM Neural Networks via Non-reduced Order Approach

  • Conference paper
  • First Online:
Simulation Tools and Techniques (SIMUtools 2020)

Included in the following conference series:

Abstract

The present paper is studying a class of inertial BAM neural networks with general activations and delays. With the help of the non-reduced order method and designing some useful Lyapunov functions, criterions ensuring the exponential stability of the investigated network system are proposed, the obtained conditions are essentially new and complement previously stability results. Moreover, a simulated example is also presented in order to support the established fruits.

B. Li—This work was supported by Social science fund project of Jiangsu Institute of Technology (NO: KYY17504), Guizhou University of Finance and Economics (NO: 2018YJ19, 2019XYB21).

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Kosko, B.: Adaptive bidirectional associative memories. Appl. Opt. 26, 4947–4960 (1987)

    Article  Google Scholar 

  2. Kosko, B.: Bidirectional associative memories. IEEE Trans. Syst. Man Cybern. 18, 49–60 (1988)

    Article  MathSciNet  Google Scholar 

  3. Cao, J., Wang, L.: Exponential stability and periodic oscillatory solution in BAM networks with delays. IEEE Trans. Neural Netw. 13, 457–463 (2002)

    Article  Google Scholar 

  4. Huang, C., Yang, Z., Yi, T., et al.: On the basins of attraction for a class of delay differential equations with non-monotone bistable nonlinearities. J. Differ. Equ. 256, 2101–2114 (2014)

    Article  MathSciNet  Google Scholar 

  5. Huang, C., Long, X., Cao, J.: Stability of antiperiodic recurrent neural networks with multiproportional delays. Math. Methods Appl. Sci. 43(9), 6093–6102 (2020)

    Article  MathSciNet  Google Scholar 

  6. Duan, L.: Existence and global exponential stability of pseudo almost periodic solutions of a general delayed BAM neural networks. J. Syst. Sci. Complex 31, 608–620 (2018)

    Article  MathSciNet  Google Scholar 

  7. Wang, J., Chen, X., Huang, L.: The number and stability of limit cycles for planar piecewise linear systems of node-saddle type. J. Math. Anal. Appl. 469(1), 405–427 (2019)

    Article  MathSciNet  Google Scholar 

  8. Huang, C., Zhang, H.: Periodicity of non-autonomous inertial neural networks involving proportional delays and non-reduced order method. Int. J. Biomath. 12, 1950016 (2019)

    Article  MathSciNet  Google Scholar 

  9. Xu, C., Li, P., Pang, Y.: Global exponential stability for interval general bidirectional associative memory (BAM) neural networks with proportional delays. Math. Methods Appl. Sci. 39(18), 5720–5731 (2016)

    Article  MathSciNet  Google Scholar 

  10. Wang, L., Ding, X., Li, M.: Global asymptotic stability of a class of generalized BAM neural networks with reaction-diffusion terms and mixed time delays. Neurocomputing 321, 251–265 (2018)

    Article  Google Scholar 

  11. Lakshmanan, S., Park, J.H., et al.: Stability criteria for BAM neural networks with leakage delays and probabilistic time-varying delays. Appl. Math. Comput. 219, 9408–9423 (2013)

    MathSciNet  MATH  Google Scholar 

  12. Wei, X., Qiu, Z.: Anti-periodic solutions for BAM neural networks with time delays. Appl. Math. Comput. 221, 221–229 (2013)

    MathSciNet  MATH  Google Scholar 

  13. Duan, L., Huang, L., Guo, Z., Fang, X.: Periodic attractor for reaction-diffusion high-order Hopfield neural networks with time-varying delays. Comput. Math. Appl. 73(2), 233–245 (2017)

    Article  MathSciNet  Google Scholar 

  14. Chen, C., Li, L., Peng, H., Yang, Y.: Fixed-time synchronization of memristor-based BAM neural networks with time-varying discrete delay. Neural Netw. 96, 47–54 (2017)

    Article  Google Scholar 

  15. Duan, L., Shi, M., Huang, L.: New results on finite-/fixed-time synchronization of delayed diffusive fuzzy HNNs with discontinuous activations. Fuzzy Sets Syst. (2020). https://doi.org/10.1016/j.fss.2020.04.016

    Article  Google Scholar 

  16. Gupta, P., Majee, N., Roy, A.: Stability and Hopf-bifurcation analysis of delayed BAM neural network under dynamic thresholds with distributed delay Nonlinear Anal. Model. Control 14, 435–461 (2009)

    MATH  Google Scholar 

  17. Huang, C., Zhang, H., Cao, J., Hu, H.: Stability and Hopf bifurcation of a delayed prey–predator model with disease in the predator. nt. J. Bifur. Chaos 29(07), 1950091 (2019)

    Article  MathSciNet  Google Scholar 

  18. Babcock, K.L., Westervelt, R.M.: Stability and dynamics of simple electronic neural networks with added inertia. Phys. D 23, 464–469 (1986)

    Article  Google Scholar 

  19. Angelaki, D.E., Correia, M.J.: Models of membrane resonance in pigeon semicircular canal type II hair cells. Biol. Cybern. 65(1), 1–10 (1991)

    Article  Google Scholar 

  20. Shi, M., Guo, J., Fang, X., Huang, C.: Global exponential stability of delayed inertial competitive neural networks. Adv. Differ. Equ. 2020(87), 1–12 (2020)

    MathSciNet  Google Scholar 

  21. Li, X., Li, X., Hu, C.: Some new results on stability and synchronization for delayed inertial neural networks based on non-reduced order method. Neural Netw. 96, 91–100 (2017)

    Article  Google Scholar 

  22. Huang, C., Liu, B.: New studies on dynamic analysis of inertial neural networks involving non-reduced order method. Neurocomputing 325, 283–287 (2019)

    Article  Google Scholar 

  23. Hu, H., Zou, X.: Existence of an extinction wave in the Fisher equation with a shifting habitat. Proc. Amer. Math. Soc. 145(11), 4763–4771 (2017)

    Article  MathSciNet  Google Scholar 

  24. Abdurahman, A., Jiang, H.: Nonlinear control scheme for general decay projective synchronization of delayed memristor-based BAM neural networks. Neurocomputing 357, 282–291 (2019)

    Article  Google Scholar 

  25. Zhang, J., Huang, C.: Dynamics analysis on a class of delayed neural networks involving inertial terms. Adv. Differ. Equ. 2020(1), 1–12 (2020)

    Article  MathSciNet  Google Scholar 

  26. Wang, J., Huang, C., Huang, L.: Discontinuity-induced limit cycles in a general planar piecewise linear system of saddle-focus type. Nonlinear Anal. Hybrid Syst. 33, 162–178 (2019)

    Article  MathSciNet  Google Scholar 

  27. Qi, J., Li, C., Huang, T.: Stability of inertial BAM neural network with time-varying delay via impulsive control. Neurocomputing 161, 162–167 (2015)

    Article  Google Scholar 

  28. Zhang, Z., Quan, Z.: Global exponential stability via inequality technique for inertial BAM neural networks with time delays. Neurocomputing 151, 1316–1326 (2015)

    Article  Google Scholar 

  29. Zhang, W., Huang, T., Li, C., Yang, J.: Robust stability of inertial BAM neural networks with time delays and uncertainties via impulsive effect. Neural Process. Lett. 48, 245–256 (2018)

    Article  Google Scholar 

  30. Maharajan, C., Raja, R., Cao, J., Rajchakit, G.: Novel global robust exponential stability criterion for uncertain inertial-type BAM neural networks with discrete and distributed time-varying delays via Lagrange sense. J. Franklin Inst. 355, 4727–4754 (2018)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Business School, Jiangsu University of Technology, Changzhou, China

    Bingnan Tang

  2. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, China

    Bingjun Li

  3. School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan, China

    Jianjun Jiao & Fengjun Di

Authors
  1. Bingnan Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bingjun Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jianjun Jiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Fengjun Di
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Embry-Riddle Aeronautical University, Daytona Beach, FL, USA

    Houbing Song

  2. School of Astronautics and Aeronautic, UESTC, Chengdu, China

    Dingde Jiang

Rights and permissions

Reprints and permissions

Copyright information

© 2021 ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Tang, B., Li, B., Jiao, J., Di, F. (2021). On Exponential Stability for Delayed Inertial BAM Neural Networks via Non-reduced Order Approach. In: Song, H., Jiang, D. (eds) Simulation Tools and Techniques. SIMUtools 2020. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 369. Springer, Cham. https://doi.org/10.1007/978-3-030-72792-5_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-72792-5_21

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-72791-8

  • Online ISBN: 978-3-030-72792-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation