@Article{JNMA-3-3,
author = {Zhen, Xiaolin and Yuting, Ding},
title = {Hopf Bifurcation Analysis for a Delayed Business Cycle Model — The Equivalence of Multiple Time Scales Versus Center Manifold Reduction Methods},
journal = {Journal of Nonlinear Modeling and Analysis},
year = {2021},
volume = {3},
number = {3},
pages = {403--419},
abstract = {<p style="text-align: justify;">In this paper, we study the Hopf bifurcation of a model with a
second order term, which is the business cycle model with delay. Multiple
time scales method, which is mainly used by the engineering researchers, and
center manifold reduction method, which is mainly used by researchers from
mathematical society, are used to derive the two types of normal forms near
the Hopf critical point. A comparison between the two methods shows that
the two normal forms are equivalent. Scholars can derive the normal form by
choosing appropriate methods according to their actual demands. Moreover,
bifurcation analysis and numerical simulations are given to verify the analytical
predictions.</p>},
issn = {2562-2862},
doi = {https://doi.org/10.12150/jnma.2021.403},
url = {https://global-sci.com/article/87980/hopf-bifurcation-analysis-for-a-delayed-business-cycle-model-the-equivalence-of-multiple-time-scales-versus-center-manifold-reduction-methods}
}