Date of Graduation
Fall 2017
Degree
Master of Science in Mathematics
Department
Mathematics
Committee Chair
Jorge Rebaza
Abstract
In bifurcation theory, there is a theorem (called Sotomayor's Theorem) which proves the existence of one of three possible bifurcations of a given system, provided that certain conditions of the system are satisfied. It turns out that there is a "similar" theorem for proving the existence of what is referred to as a Bogdanov-Takens bifurcation. The author is only aware of one reference that has the proof of this theorem. However, most of the details were left out of the proof. The contribution of this thesis is to provide the details of the proof on the existence of Bogdanov-Takens bifurcations.
Keywords
Bogdanov-Takens bifurcation, bifurcation, dynamical systems, Hopf bifurcation, Saddle-Node bifurcation
Subject Categories
Dynamic Systems | Non-linear Dynamics | Ordinary Differential Equations and Applied Dynamics
Copyright
© Zachary Deskin
Recommended Citation
Deskin, Zachary, "On the Existence of Bogdanov-Takens Bifurcations" (2017). MSU Graduate Theses/Dissertations. 3196.
https://bearworks.missouristate.edu/theses/3196
Open Access
Included in
Dynamic Systems Commons, Non-linear Dynamics Commons, Ordinary Differential Equations and Applied Dynamics Commons
