Date of Graduation
Master of Science in Mathematics
Lienard system, van der Pol system, van der Pol equation, autonomous system, limit cycle, Poincare-Bendixson, bifurcation, Hopf bifurcation
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.
© Robert S. Brown
Brown, Robert S., "Autonomous Systems and the van der Pol Equation" (2011). MSU Graduate Theses. 2993.