Thesis Title

An Introduction to Singularity Bifurcations

Author

Jeremy Nation

Date of Graduation

Summer 2005

Degree

Master of Science in Mathematics

Department

Mathematics

Committee Chair

Jorge Rebaza

Keywords

dynamical systems, bifurcations, singularity, stability, linearization

Subject Categories

Mathematics

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.

Copyright

© Jeremy Nation

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Dissertation/Thesis

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