On a weakly forced third order weakly non-linear system

The behaviour of a weakly non-linear third order system under a weak forcing function is considered. By the method of multiple time scales, it is found that the amplitude of the forced oscillation increases with the amplitude of the forcing function until a critical value is reached. Beyond this value, stable oscillations exist whose amplitude decreases with the amplitude of the forcing function but which are superimposed on a constant of increasing magnitude.