Autonomous Systems and the van der Pol Equation

Author

Robert S. Brown

Date of Graduation

Fall 2011

Degree

Master of Science in Mathematics

Department

Mathematics

Committee Chair

Shouchuan Hu

Abstract

The aim of this paper was to examine autonomous dynamical systems qualitatively, especially the Lienard and van der Pol systems. It was found that under certain conditions, solutions of a Lienard system tend to a periodic orbit, and that this orbit is a result of a bifurcation. In particular, this paper used theorems by Poincare and Levinson to prove that the Lienard system, and thus the van der Pol system, has a limit cycle which is unique.

Keywords

Lienard system, van der Pol system, van der Pol equation, autonomous system, limit cycle, Poincare-Bendixson, bifurcation, Hopf bifurcation

Subject Categories

Mathematics

Copyright

© Robert S. Brown

Recommended Citation

Brown, Robert S., "Autonomous Systems and the van der Pol Equation" (2011). MSU Graduate Theses. 2993.
https://bearworks.missouristate.edu/theses/2993