Modeling the innovation resonance in industrialized regions

The main objective of this article is to provide a rationale for mathematical models describing the innovation resonance in industrialized regions. The article presents a thorough analysis of trends in the development of Russian industrialized regions, which is then used as the basis to advance and test several hypotheses, such as the hypothesis of uneven economic development in different types of industrialized regions (regions strengthening their industrial status, newly industrialized regions and deindustrialized regions), hypothesis of individual characteristics in the development of certain types of industrialized regions, hypothesis of the state acting as catalyst in innovation dynamics, hypothesis of innovation resonance existing in economic system. The authors propose the methodology of innovation resonance, describe the conditions required for the emergence of resonance in the economic system, and provide a rationale for the types of resonance response. The main methods used in this article are as follows: resonance control method, reproduction method, methods of economic and mathematical modeling. The authors propose a mathematical formalization for the mechanism of innovation resonance in the regional industrial system, including: a) A model for generating investment by industrial sectors and reproduction sectors; b) Dynamic multi-sector reproduction model; c) Adaptive management model for innovative self-development of the regional industrial system; g) A model for the sustainability of innovation dynamics and expanded reproduction. The authors study the innovation resonance in Russian industrialized regions. In the context of innovation resonance, the authors review the functional industrial policy of a typical industrialized region and resonance responses related to its implementation. The results of the study presented in the article can be used in substantiating the mechanisms of regional industrial policy, and to assess the regulatory impact of existing regulatory and legal acts