An Introduction to Singularity Bifurcations
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
Recommended Citation
Nation, Jeremy, "An Introduction to Singularity Bifurcations" (2005). MSU Graduate Theses/Dissertations. 1621.
https://bearworks.missouristate.edu/theses/1621
