Hopf Bifurcation Analysis for a Delayed Business Cycle Model — The Equivalence of Multiple Time Scales Versus Center Manifold Reduction Methods (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, we study the Hopf bifurcation of a model with asecond order term, which is the business cycle model with delay. Multipletime scales method, which is mainly used by the engineering researchers, andcenter manifold reduction method, which is mainly used by researchers frommathematical society, are used to derive the two types of normal forms nearthe Hopf critical point. A comparison between the two methods shows thatthe two normal forms are equivalent. Scholars can derive the normal form bychoosing appropriate methods according to their actual demands. Moreover,bifurcation analysis and numerical simulations are given to verify the analyticalpredictions.