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Control theory methods for creating market structures are discussed for two cases: when market participants are pursuing aims 1) of maximal growth and 2) of maximum economic efficiency of their firms. For the first case method based on variable structure systems principles is developed. For the second case dynamic game approach is proposed based on computation of Nash–Cournot and Stackelberg strategies with the help of Z-transform.

The paper considers the basic model of competitive interactions and its use for the analysis and description of social processes. The peculiarity of the model is that it describes the interaction of several competing actors, while actors can vary the strategy of their actions, in particular, form coalitions to jointly counter a common enemy. As a result of modeling, various modes of competitive interaction were identified, their classification was conducted, and their features were described. In the course of the study, the attention is paid to the so-called “rough” (according to A.A. Andronov) cases of the implementation of competitive interaction, which until now have rarely been considered in the scientific literature, but are quite common in real life. Using a basic mathematical model, the conditions for the implementation of various modes of competitive interactions are considered, the conditions for the transition from one mode to another are determined, examples of the implementation of these modes in the economy, social and political life are given. It is shown that with a relatively low level of competition, which is non-antagonistic in nature, competition can lead to an increase in the activity of interacting actors and to overall economic growth. Moreover, in the presence of expanding resource opportunities (as long as such opportunities remain), this growth may have a hyperbolic character. With a decrease in resource capabilities and increased competition, there is a transition to an oscillatory mode, when weaker actors unite to jointly counteract stronger ones. With a further decrease in resource opportunities and increased competition, there is a transition to the formation of stable hierarchical structures. At the same time, the model shows that at a certain moment there is a loss of stability, the system becomes “rough” according to A.A. Andronov and sensitive to fluctuations in parameter changes. As a result, the existing hierarchies may collapse and be replaced by new ones. With a further increase in the intensity of competition, the actor-leader completely suppresses his opponents and establishes monopolism. Examples from economic, social, and political life are given, illustrating the patterns identified on the basis of modeling using the basic model of competition. The obtained results can be used in the analysis, modeling and forecasting of socioeconomic and political processes.

The article proposes a space-time approach to modeling the diffusion of information and communication technologies based on the Fisher –Kolmogorov– Petrovsky – Piskunov equation, in which the diffusion kinetics is described by the Bass model, which is widely used to model the diffusion of innovations in the market. For this equation, its equilibrium positions are studied, and based on the singular perturbation theory, was obtained an approximate solution in the form of a traveling wave, i. e. a solution that propagates at a constant speed while maintaining its shape in space. The wave speed shows how much the “spatial” characteristic, which determines the given level of technology dissemination, changes in a single time interval. This speed is significantly higher than the speed at which propagation occurs due to diffusion. By constructing such an autowave solution, it becomes possible to estimate the time required for the subject of research to achieve the current indicator of the leader.

The obtained approximate solution was further applied to assess the factors affecting the rate of dissemination of information and communication technologies in the federal districts of the Russian Federation. Various socio-economic indicators were considered as “spatial” variables for the diffusion of mobile communications among the population. Growth poles in which innovation occurs are usually characterized by the highest values of “spatial” variables. For Russia, Moscow is such a growth pole; therefore, indicators of federal districts related to Moscow’s indicators were considered as factor indicators. The best approximation to the initial data was obtained for the ratio of the share of R&D costs in GRP to the indicator of Moscow, average for the period 2000–2009. It was found that for the Ural Federal District at the initial stage of the spread of mobile communications, the lag behind the capital was less than one year, for the Central Federal District, the Northwestern Federal District — 1.4 years, for the Volga Federal District, the Siberian Federal District, the Southern Federal District and the Far Eastern Federal District — less than two years, in the North Caucasian Federal District — a little more 2 years. In addition, estimates of the delay time for the spread of digital technologies (intranet, extranet, etc.) used by organizations of the federal districts of the Russian Federation from Moscow indicators were obtained.