The article reflects a study aimed at using a parallel computing system for automated retrieval and visualization of cycles of a quadratic system of two differential equations. The study was conducted in the sevendimensional space of parameters - system coefficients and initial data of the Cauchy problem. It is very important for sustainable operation of transport systems. To implement the calculations, supercomputers of Moscow State University were remotely used. Visualization of the results carried out on Hewlett Packard personal computers. The developed software model is applicable to weaning and visualization of cycles for different systems of two differential equations.