Time-Delay-Induced Hopf Bifurcation in a Fractional-Order Ecological System
Abstract
In this paper, we investigate a fractional-order delayed dynamical system. Taking the time delay τ as the bifurcation parameter, we establish that the equilibrium is asymptotically stable for all τ<τ0, and a Hopf bifurcation occurs as τ passes through the critical value τ0. We derive the characteristic equation and verify the transversality condition, which identifies the onset of oscillations and characterizes the stability of the emerging periodic solutions. Numerical experiments carried out in MATLAB with a predictor–corrector scheme support the analysis and illustrate the resulting oscillatory behavior.
- Published
- 13 February 2026
- Volume
- 2026 (2026)
- License
- CC BY 3.0
Copyright © 2026 Canan Çelik, Kübra DeÄŸerli. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
C. Çelik, K. DeÄŸerli, Time-Delay-Induced Hopf Bifurcation in a Fractional-Order Ecological System, Commun. Math. Biol. Neurosci. 2026 (2026), 12. https://doi.org/10.28919/cmbn/9725
BibTeX
@article{Çelik2026,
author = {Çelik, Canan and DeÄŸerli, Kübra},
title = {Time-Delay-Induced Hopf Bifurcation in a Fractional-Order Ecological System},
journal = {Commun. Math. Biol. Neurosci.},
volume = {2026},
year = {2026},
pages = {12},
doi = {10.28919/cmbn/9725}
}