Hopf Bifurcations and Horseshoes Especially Applied to the Brusselator

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.

Name thesis:degree_name

MS

Grantor dc:publisher

Brigham Young University - Provo

Author dc:creator

• Jones, Steven R.

• Hopf bifurcation
• horseshoe
• Brusselator
• Mathematics

Language dc:language

English

Repository record dc:identifier

https://scholarsarchive.byu.edu/etd/635

OAI identifier oai:identifier

oai:scholarsarchive.byu.edu:etd-1634