In this paper we explore bifurcations, in particular the Hopf bifurcation. We study this especially in connection with the Brusselator, which is a model of certain chemical reaction-diffusion systems. After a thorough exploration of what a bifurcation is and what classifications there are, we give graphic representations of an occurring Hopf bifurcation in the Brusselator. When an additional forcing term is added, behavior changes dramatically. This includes the introduction of a horseshoe in the time map as well as a strange attractor in the system.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Jones, Steven R., "Hopf Bifurcations and Horseshoes Especially Applied to the Brusselator" (2005). Theses and Dissertations. 635.
Hopf bifurcation, horseshoe, Brusselator