Resonant oscillations and fractal basin boundaries of a particle in a φ6 potential

This paper considers the dynamics of a periodically forced particle in a φ6 potential. Harmonic, subharmonic and superharmonic oscillatory states are obtained using the multiple time scales method. From the Melnikov theory, we derive the analytical criteria for the occurrence of transverse intersections on the surface of homoclinic and heteroclinic orbits both for the three potential well case and a single potential well case. Our analytical investigations are complemented by the numerical simulations from which we show the fractality of the basins of attraction.