Subharmonic solutions of the duffing equation with large non-linearity1

The subharmonic solutions of order $\text{1}\text{3}$ of the damped Duffing equation are determined in a suitable parametric form, following the procedure recently developed in [8, 9], and are compared with the results obtained by direct numerical integration of the same equation, carried out with respect to the time with the Runge-Kutta method. It can be deduced that the analytical solution gives satisfactory results in the approximation of the ‘predominantly’ subharmonic solutions of the above equation, even if the non-linearity of the system is very large.