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Journal of Applied Mathematics and Computation

ISSN Online: 2576-0653 ISSN Print: 2576-0645 CODEN: JAMCEZ
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ArticleOpen Access http://dx.doi.org/10.26855/jamc.2026.06.005

Bifurcation Analysis of a Simplified BT Model

Suqi Ma*, Bohan Ma, Huailei Wang

Department of Mathematics, China Agricultural University, Beijing 100083, China.

*Corresponding author:Suqi Ma

Published: June 30, 2026

Abstract

A simplified BT model is investigated with delay feedback control. With delay effects, the system manifests various kinds of bifurcation in the two-parameter plane. The normal form near the BT point is computed by applying the perturbation scheme combined with the center manifold theory analysis. The two BT points are found on the Hopf line, which brings new bifurcation phenomena beyond. The bifurcation curve near the BT point is obtained by continuing the homoclinic bifurcation while varying the time delay. With a fixed time delay, the complex dynamics is explored by varying free parameters in the circle with a small radius. The dynamical analysis is completed using the hand tools of DDE-Bfitool software, which is an artificial technique for conducting equilibrium analysis in number and bifurcation. The continuation of Bautin bifurcation curves is performed near the codimension-two singularity of Generalized Hopf points, which is the bonus with the Lyapunov coefficient attaining a nearly zero value. Simultaneously, the homoclinic continuation is completed, and the BT bifurcation happens at the circle. The interesting phenomena of multiple cycles and homoclinic solution coexistence are explored, which are ubiquitous in the dynamical analysis of the whole system bifurcation behavior.

Keyword

BT model; homoclinic bifurcation; delay feedback control; generalized Hopf bifurcation

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Copyright

© 2026 by the author(s).
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How to cite this paper

Bifurcation Analysis of a Simplified BT Model

How to cite this paper: Suqi Ma, Bohan Ma, Huailei Wang. (2026) Bifurcation Analysis of a Simplified BT Model. Journal of Applied Mathematics and Computation10(2), 103-112.

DOI: http://dx.doi.org/10.26855/jamc.2026.06.005