SUMMARY
Content. Software systems are used in a variety of branches of life and human activities, but they are most widely used in industries where it is necessary to work with many routine operations – this applies to industry, production, transportation, training and info communications. Of course, in the process of exploiting these systems there is an evolutionary aging of the different types of security. This trend leads to a deterioration of high-speed, information-communication, graphic, time and other characteristics, up to the complete failure of the software system. The subject of the article is aimed to the design of ergative systems, project management and programs for re-designing or improving these systems. Reengineering allows the system to evolve, by making positive changesto its structure in order to improve operational characteristics and technical support.Objective. To form a representation of the estimation of resource cost parameters for the reengineering of software systems with the help of a mathematical tools for describing design models.Method. The idea of the article is based on the Boehm method and the principles of building an Archimedes spiral. Author’s research led to the idea of combining Boehm and Archimedes structures, adapting them to the software engineering methodology and transferring them to a cylindrical coordinate system. The basis of the obtained models is laid spiral principle of the organization of the reference.Results. The article deals with the process of creating and visualizing mathematical models in relation to the process of reengineering software systems. Transactions with these models can occur in projections of time and cost, in the isometric projection of software components, and in the logarithmic projection of lines of software code.Conclusions. For the first time, idealized models of reengineering have been formed, which will allow to increase the accuracy of cost estimation from the redesign of software systems. The model of cost visualization for reprogramming of software systems has been improved, which will increase the efficiency of forecasting the order of expenses. For the first time dependencies were obtainedon the construction of the graphical cost model trajectory from the introduced reengineering automation coefficient and the similarity coefficient of the components that would make changes to the configuration of the model. The proposed idealized models for reengineering of software system security are evolutionary spirals, which are constructed in a cylindrical coordinate system. Reengineering, which will be accomplished with the help of developed idealized reengineering models, will not only reduce the cost of reprogrammingsoftware systems, but also increase the efficiency of technical support, increase the life cycle of software systems which are already in service and overcome the contradictions between the rapid pace of development of science, technology and processes of designing new software systems.