@article{Liu2026, 
author = {Shouzong Liu and Tingting Lu and Jianing Qin and Yaxin Niu},
title = {Hopf bifurcation analysis of a modified Brusselator model with sub-interval distributed delay},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {3},
pages = {6569-6591},
keywords = {Brusselator model, sub-interval distributed delay, Hopf bifurcation, stability},
url = {https://www.sciopen.com/article/10.3934/math.2026272},
doi = {10.3934/math.2026272},
abstract = {In this paper, a modified Brusselator model incorporating a moderated autocatalytic term and a sub-interval distributed delay is investigated. The existence and uniqueness of a positive equilibrium are first established, together with explicit conditions for its local asymptotic stability. By deriving and analyzing the associated characteristic equation, two distinct Hopf bifurcation mechanisms are rigorously identified: one induced by variations in the delay center    τ and the other triggered by changes in the delay distribution width    ε. Sufficient conditions for the existence of two Hopf bifurcation branches in the    (  τ  ,  ε  )-parameter plane are obtained, and the corresponding transversality conditions are verified. Finally, numerical simulations are carried out to validate the theoretical results. The results reveal a clear destabilizing role of the delay center and a stabilizing, smoothing effect of the delay width, which highlights the important role of distributed delays in shaping the dynamical behavior of autocatalytic reaction systems.}
}