Date of Graduation

Fall 2017

Degree

Master of Science in Mathematics

Department

Mathematics

Committee Chair

Jorge Rebaza

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

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.

Copyright

© Zachary Deskin

Open Access

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