Sigmoid-function Based Fixed-time Stability of Delayed Nonlinear Dynamic Systems
Research Article  ·  Published: 27 February 2026
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Journal of Nonlinear Dynamics and Applications
Volume 2, Issue 1, 2026: 13-19
Research Article Open Access

Sigmoid-function Based Fixed-time Stability of Delayed Nonlinear Dynamic Systems

1 School of Mathematics and Statistics, South-Central Minzu University, Wuhan 430074, China
2 Department of Mathematics, Nazarbayev University, Nur-Sultan 010000, Kazakhstan
3 Department of Information and Electronic Engineering, International Hellenic University, Thessaloniki, Greece
4 Departamento de Matemática, Facultad de Ciencias Básicas, Universidad Metropolitana de Ciencias de la Educación, Josó Pedro Alessandri 774, Santiago 7760197, Chile
* Corresponding Author: Guodong Zhang, [email protected]
Volume 2, Issue 1

Article Information

Abstract

This paper investigates fixed-time stability of delayed nonlinear dynamic systems. At first, by designing an inequality with sigmoid-function, a new kind of fixed-time stability lemma is constructed. Then, as an application, the new proposed lemma is applied to discuss fixed-time stabilization(FT) for a kind of delayed neural networks. At last, simulations are also given to show the effectiveness of the derived results.

Graphical Abstract

Sigmoid-function Based Fixed-time Stability of Delayed Nonlinear Dynamic Systems

Keywords

fixed-time stability nonlinear dynamic systems fixed-time stabilization sigmoid-function time delays

Data Availability Statement

Data will be made available on request.

Funding

This work was supported by the National Science Foundation of China under Grant 62476292, and the Fundamental Research Funds for Central University of South-Central Minzu University under Grant CZQ24020.

Conflicts of Interest

The authors declare no conflicts of interest.

AI Use Statement

The authors declare that no generative AI was used in the preparation of this manuscript.

Ethical Approval and Consent to Participate

Not applicable.

References

  1. Polyakov, A. (2012). Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Transactions on Automatic Control, 57(8), 2106-2110.
    [CrossRef] [Google Scholar]
  2. Yang, X., Lam, J., Ho, D. W., & Feng, Z. (2017). Fixed-time synchronization of complex networks with impulsive effects via nonchattering control. IEEE Transactions on Automatic Control, 62(11), 5511-5521.
    [CrossRef] [Google Scholar]
  3. Kong, F., Zhu, Q., Sakthivel, R., & Mohammadzadeh, A. (2021). Fixed-time synchronization analysis for discontinuous fuzzy inertial neural networks with parameter uncertainties. Neurocomputing, 422, 295-313.
    [CrossRef] [Google Scholar]
  4. Ma, Z. F., Tong, D. B., Chen, Q. Y., & Zhou, W. N. (2025). Fixed/prescribed-time synchronization and energy consumption for Kuramoto-oscillator networks. IEEE Transactions on Cybernetics, 55(7), 3379-3389.
    [CrossRef] [Google Scholar]
  5. Hu, C., He, H., & Jiang, H. (2021). Fixed/preassigned-time synchronization of complex networks via improving fixed-time stability. IEEE Transactions on Cybernetics, 51(6), 2882-2892.
    [CrossRef] [Google Scholar]
  6. Aouiti, C., Hui, Q., Jallouli, H., & Moulay, E. (2021). Fixed-time stabilization of fuzzy neutral-type inertial neural networks with time-varying delay. Fuzzy Sets and Systems, 411, 48-67.
    [CrossRef] [Google Scholar]
  7. Hu, X., Wang, L., Zhang, C. K., Wan, X., & He, Y. (2023). Fixed-time stabilization of discontinuous spatiotemporal neural networks with time-varying coefficients via aperiodically switching control. Science China Information Sciences, 66(5), 152204.
    [CrossRef] [Google Scholar]
  8. Zhang, G. D., & Cao, J. D. (2023). New results on fixed/predefined-time synchronization of delayed fuzzy inertial discontinuous neural networks: Non-reduced order approach. Applied Mathematics and Computation, 440, 127671.
    [CrossRef] [Google Scholar]
  9. Zhou, X., Zhang, G., Wang, L., & Xiao, Q. (2026). Novel results on fixed-time stabilization and synchronization for delayed memristive inertial neural networks via aperiodically switching control. Communications in Nonlinear Science and Numerical Simulations, 156, 109683. https://10.1016/j.cnsns.2026.109683
    [Google Scholar]
  10. Qiao, Y., Tohti, R., Lu, B. L., Abdurahman, A., & Jiang, H. J. (2026). Internal and boundary control-based fixed-time synchronization for stochastic impulsive reaction-diffusion complex networks. Chaos, Solitons & Fractals, 206, 117910.
    [CrossRef] [Google Scholar]
  11. Forti, M., Grazzini, M., Nistri, P., & Pancioni, L. (2006). Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipschitz activations. Physica D: Nonlinear Phenomena, 214(1), 88-99.
    [CrossRef] [Google Scholar]
  12. Clarke, F. H., Ledyaev, Yu. S., Stern, R. J., & Wolenski, R. R. (1998). A short course in control theory. In Nonsmooth analysis and control theory (pp. 177–256). Springer.
    [CrossRef] [Google Scholar]

Cited By (1)

  1. Zhongtao He, Guodong Zhang, Shiping Wen. Fixed/predefined-time stabilization based on hyperbolic cosine function for memristive neural networks with mixed delays. Franklin Open, 2026 , 15 .
    [CrossRef]
* Citation data provided by Crossref Cited-by.

Cite This Article

APA Style
Zhang, G., Kashkynbayev, A., Gerontitis, D. K., & Chiu, K. S. (2026). Sigmoid-function Based Fixed-time Stability of Delayed Nonlinear Dynamic Systems. Journal of Nonlinear Dynamics and Applications, 2(1), 13–19. https://doi.org/10.62762/JNDA.2026.431637
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TY  - JOUR
AU  - Zhang, Guodong
AU  - Kashkynbayev, Ardak
AU  - Gerontitis, Dimitrios K.
AU  - Chiu, Kuo-Shou
PY  - 2026
DA  - 2026/02/27
TI  - Sigmoid-function Based Fixed-time Stability of Delayed Nonlinear Dynamic Systems
JO  - Journal of Nonlinear Dynamics and Applications
T2  - Journal of Nonlinear Dynamics and Applications
JF  - Journal of Nonlinear Dynamics and Applications
VL  - 2
IS  - 1
SP  - 13
EP  - 19
DO  - 10.62762/JNDA.2026.431637
UR  - https://www.icck.org/article/abs/JNDA.2026.431637
KW  - fixed-time stability
KW  - nonlinear dynamic systems
KW  - fixed-time stabilization
KW  - sigmoid-function
KW  - time delays
AB  - This paper investigates fixed-time stability of delayed nonlinear dynamic systems. At first, by designing an inequality with sigmoid-function, a new kind of fixed-time stability lemma is constructed. Then, as an application, the new proposed lemma is applied to discuss fixed-time stabilization(FT) for a kind of delayed neural networks. At last, simulations are also given to show the effectiveness of the derived results.
SN  - 3069-6313
PB  - Institute of Central Computation and Knowledge
LA  - English
ER  - 
BibTeX Format
Compatible with LaTeX, BibTeX, and other reference managers
@article{Zhang2026Sigmoidfun,
  author = {Guodong Zhang and Ardak Kashkynbayev and Dimitrios K. Gerontitis and Kuo-Shou Chiu},
  title = {Sigmoid-function Based Fixed-time Stability of Delayed Nonlinear Dynamic Systems},
  journal = {Journal of Nonlinear Dynamics and Applications},
  year = {2026},
  volume = {2},
  number = {1},
  pages = {13-19},
  doi = {10.62762/JNDA.2026.431637},
  url = {https://www.icck.org/article/abs/JNDA.2026.431637},
  abstract = {This paper investigates fixed-time stability of delayed nonlinear dynamic systems. At first, by designing an inequality with sigmoid-function, a new kind of fixed-time stability lemma is constructed. Then, as an application, the new proposed lemma is applied to discuss fixed-time stabilization(FT) for a kind of delayed neural networks. At last, simulations are also given to show the effectiveness of the derived results.},
  keywords = {fixed-time stability, nonlinear dynamic systems, fixed-time stabilization, sigmoid-function, time delays},
  issn = {3069-6313},
  publisher = {Institute of Central Computation and Knowledge}
}

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CC BY Copyright © 2026 by the Author(s). Published by Institute of Central Computation and Knowledge. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
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