An Introduction to Singularity Bifurcations
Date of Graduation
Master of Science in Mathematics
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.
dynamical systems, bifurcations, singularity, stability, linearization
© Jeremy Nation
Nation, Jeremy, "An Introduction to Singularity Bifurcations" (2005). MSU Graduate Theses. 1621.