Self-oscillating modes in control systems of computer networks quite negatively affect the characteristics of these networks so the investigation of parameters of self-oscillations as well as self-oscillations areas is actual. But due to the non-linear nature of usually constructed mathematical models the study of self-oscillations areas and parameters are extremely labor-intensive. It is of interest to obtain a so-called parametric portrait describing the zones of occurrence of self-oscillations depending on the value of the parameters: one parameter (two-dimensional graph), two parameters (three-dimensional graph), and so on. Such a parametric portrait allows us to purposefully manage the characteristics of the investigated control system. The paper describes a parametric study technique based on the method of harmonic linearization because in the standard mathematical model based on ordinary linearization by Taylor expansion a self-oscillation regime disappears (due to Taylor expansion linearization). To verify the theoretical results obtained, simulation is used. In addition, it is proposed to use the computer algebra system for analytical calculations. For this, the criteria for choosing software were formulated. Based on these criteria, a set of software for analytical and numerical calculations was proposed.