Background:  The paper presents the theoretical basis for the proposal of modeling of the dynamics of the modern cities’ development by the use of a properly constructed synthetic indicator. Additionally to the possibility of the quantification of the development of social and economic systems of cities, its implementation allows the identification of nonlinear processes as phase transitions, which occur e.g. under influence of technological and social innovations. The economic and physical approach to this allows to learn more about the nature of these processes and to set new instruments supporting the management of urban areas in conditions of an increasing competiveness. 

Methods: The mathematical modeling of social and economical processes and economical and physical approach to dynamics of systems of nonlinear development.

Results and conclusions: Based on conducted simulation researches, it can be concluded that the synthetic measure of the development of urban areas can be a good tool supporting the city management by local authorities. The economical and physical approach to the nonlinear dynamics of urban systems marks out new areas for further researches, the determination of minimum required conditions (the necessary level) for stimulation of the phase transition and the analysis of factors allowing to avoid the negative consequences of a phase transition, especially in smaller cities areas, seems to be the most important ones.