Features of the moment functions of an oscillator with parametric instability due to dichotomous noise with Erlang distribution functions

We study stability of the periodic solutions of a linear undamped oscillator with frequency modulated by dichotomous noise whose statistic is determined by the Erlang distribution. It is shown that the amplitudes of harmonic oscillations of such an oscillator increase with time at different rates determined by the ratio of the oscillator eigenfrequency to the characteristic frequency of dichotomous noise. To solve the problem, we use a finite system of closed equations with respect to the moment functions, which was obtained without assumption on the quasi-Gaussianity and delta-correlatedness of the studied process.