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Abstract. Present study is devoted to the development of competition life cycle mathematical model in the closed business community with limited resources. Growth of each agent is determined by the balance of input and output resource flows: input (cash) flow W is covering the variable V and constant C costs and growth dA/dt of the agent's assets A. Value of V is proportional to assets A that allows us to write down a first order non-stationary differential equation of the agent growth. Model includes the number of such equations due to the number of agents. The amount of resources that is available for agents vary in time. The balances of their input and output flows are changing correspondingly to the different stages of the competition life cycle. According to the theory of systems, the most complete description of any object or process is the model of its life cycle. Such a model describes all stages of its development: from the appearance ("birth") through development ("growth") to extinction ("death"). The model of the evolution of an individual firm, not contradicting the economic meaning of events actually observed in the market, is the desired result from modern AVMs for applied use. With a correct description of the market, rules for participants' actions, restrictions, forecasts can be obtained, which modern mathematics and the economy can not give.

Институт экономики Уральского отделения Российской академии наук, г. Екатеринбург, Россия Л. В. ВОРОНИНА Федеральный исследовательский центр комплексного изучения Арктики имени академика Н. П. Лаверова Российской академии наук, г. Архангельск, Россия Е. В. СМИРЕННИКОВА Федеральный исследовательский центр комплексного изучения Арктики имени академика Н. П. Лаверова Российской академии наук, г. Архангельск, Россия А. В. УХАНОВА Федеральный исследовательский центр комплексного изучения Арктики имени академика Н. П. Лаверова Российской академии наук, г. Архангельск, Россия

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In age of sustainable development, strategic innovations have become the most important factor in the adaptation of national economies to dynamic global changes, encompassing trade and economic relations between the leading and developing countries of the World. At the same time, the task of this study was to reveal the complex and contradictory role of strategic innovations in the development of national economies against the background of the transformation of global value chains (GVCs). Main methods for solving the problem were empirical methods of comparative and structural analysis, as well as econometrics. The study analyzed 44 countries classified by the World Bank in the group of countries with per capita incomes below and above the average, as well as with high income. Results of the calculations made it possible to establish a highly differentiated relationship between the share of products manufactured by foreign companies operating in the host countries, on the one hand, and indicators of the dynamics of foreign direct investment (the number of researchers engaged in R&D, the number of technical specialists involved in research and development (R&D), the cost of research and development in the territory of the host countries), on the other hand. This made it possible to determine the role of strategic innovation in the adaptation of national economies. The established dependencies expand the understanding of the role of strategic innovations in the formation and further development of global value chains and their significance in evolution: from process and product innovations of individual companies to the formation of global innovation ecosystems.