Bifurcations of a Van der Pol oscillator in a double well

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.