Resonant oscillation and homoclinic bifurcation in a Φ6-Van der Pol oscillator

In this paper, we study the dynamics of a system consisting of extended Duffing–Van der Pol oscillator. Resonance and nonresonance oscillations are analyzed using the multiple scale method. From the Melnikov theorem, we obtain the condition for the existence of homoclinic bifurcation both in the case where the Φ6 potential is a bounded or unbounded double hump. A convenient demonstration of the accuracy of the method is obtained from the fractal basin boundary.