Basin boundaries with fractal and smooth accumulation properties in systems with single potential well (Q1809580)

Simulation of the equation \(\ddot{x}_\beta x +(1+F\sin\omega t)(x+x^3)=0.1 F\sin(\omega t)\) are discussed related with a bifurcation of passing two periodic solutions through saddle-node one that can lead to the complexification of a basin boundary of one periodic solution in dependence on the presence of homo- or heteroclinic solution for another periodic solution.