Complete investigation into the problem of parametric oscillations of a system in the presence of dissipation is carried out. Based on the numerical-analytical method, the boundaries of stability regions are constructed in a wide range of varying modulation coefficients and linear friction. It was implicitly assumed that the instability regions are maximal, while the actual presence of small dissipation leads to their narrowing. Modern software allows one to effectively construct the desired solutions of different classes of complex multi-parametric problems. This is achieved using the constructive algorithms based on the accelerated convergence method and continuation procedures by known parameters of the system in admissible regions of their variation.
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