Bifurcations of a Van der Pol oscillator in a double well

TL;DR

This paper investigates how the shape of a double well affects the bifurcation behavior and dynamics of a Van der Pol oscillator, revealing the importance of well geometry on stability and limit cycle phenomena.

Contribution

It introduces a detailed analysis of bifurcations in a Van der Pol oscillator with symmetric and asymmetric double wells, highlighting the impact of well shape on system dynamics.

Findings

Well shape influences fixed point stability

Limit cycles emerge and vanish with well shape changes

Symmetric and asymmetric wells exhibit distinct bifurcation patterns

Abstract

We study the changes in the phase portrait of a Van der Pol oscillator in a double well with the change in the shape of the well. Both the symmetric and asymmetric double wells are considered. We find that the shape of the well plays a very important role in the dynamics of the oscillator such as with the change in shape of the well, the stability of the fixed points of the system changes as well as limit cycles appear and are being destroyed.