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

Guodong Zhang; Ardak Kashkynbayev; Dimitrios K. Gerontitis; Kuo-Shou Chiu

doi:10.62762/JNDA.2026.431637

Volume 2, Issue 1, Journal of Nonlinear Dynamics and Applications

Volume 2, Issue 1, 2026

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Journal of Nonlinear Dynamics and Applications, Volume 2, Issue 1, 2026: 13-19

Open Access | Research Article | 27 February 2026

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

Guodong Zhang 1 *

Ardak Kashkynbayev 2

Dimitrios K. Gerontitis 3

Kuo-Shou Chiu 4

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]

DOI: 10.62762/JNDA.2026.431637

ARK: ark:/57805/jnda.2026.431637

Received: 01 September 2025, Accepted: 24 February 2026, Published: 27 February 2026

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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

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.

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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  -

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@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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