Van der Pol Oscillator – Analysis of a Non-conservative System

Abstract

The Van der Pol oscillator was introduced by Balthasar van der Pol, who was ”a famous scholar, a famous scientist, a famous administrator at the international level, he was equally well known for the clarity of his lectures (in several languages), his knowledge of the classics, his warm personality and his talents for friendship, and his love for music.” The oscillator describes the nonlinear oscillations for systems like a triode circuit, which produce self-sustained oscillations known as relaxation oscillations. Extensive studies have been done on the oscillator, for understanding it and for using it as an applied model for the heartbeat, for example. In this thesis, we will explain the nature of the oscillator from an original point of view, in the low-friction regime. First, we will give an intuitive physical explanation of the first order averaging method, a perturbation theory method, applied onto the oscillator. We will follow with an analytical approach of the first order averaging method, and we will show the mathematical complexity of it. We will conclude with the application of the first order averaging method to the Van der Pol oscillator,confirming the findings from the intuitive approach.

Presented in absentia on April 27, 2020 at "Student Research Day" at MacEwan University in Edmonton, Alberta. (Conference cancelled.) Exhibition held in the Gray Gallery at MacEwan University.

Faculty Mentor: Ion Bica

Department: Mathematics & Statistics