Self-oscillating modes in control systems of computer networks quite negatively affect the characteristics of these networks. The problem of finding the areas of self-oscillations is actual and important as the study of parameters of self-oscillations. These studies are extremely labor-intensive because of the substantial non-linear nature of the mathematical model. To investigate the self-oscillation parameters, the authors used the method of harmonic linearization. However, the previously used model with symmetric oscillations showed its limitations. In this paper, a more complex model with asymmetric oscillations is applied. For this purpose, the authors developed the program complex with both numerical analysis elements and elements of symbolic calculations.