An Introduction to Singularity Bifurcations

Jeremy Nation

Date of Graduation

Summer 2005

Degree

Master of Science in Mathematics

Department

Mathematics

Committee Chair

Jorge Rebaza

Abstract

Local bifurcations of a fixed point, where the qualitative behavior of a dynamical system changes as certain parameters vary, are the topic of this work. In particular, we study singularity bifurcations, where a drop in dimensionality accompanies the behavioral changes to the system. A rigorous theoretical framework is developed in which bifurcations can be studied, and many examples are provided to illustrate the ideas necessary to understanding local bifurcations, including: the existence and uniqueness of solutions, linearization, and stability.

Keywords

dynamical systems, bifurcations, singularity, stability, linearization

Subject Categories

Mathematics

Copyright

© Jeremy Nation

Citation-only

Dissertation/Thesis

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