Наукові горизонти (Mar 2020)
MODELING OF THE LIMIT STATES IN THE DYNAMIC SYSTEMS OF LIVING AND LIFELESS NATURE
Abstract
The article is sanctified to the exposure of the universal mathematical going to the quantitative design of dynamics systems of various physical nature. Aim of the research: To substantiate the possibility of using common approaches to the quantitative modeling of the dynamics of living and non-living systems. As a result were educed terms and ranges of application the general discrete models of development technique, dynamics of populations, economic models. It was built generalized Fibonacci model, that allows to forecast the indicated processes for the different values of parameter a prehistory γ. Quantitative comparison of the offered approaching the generalized model of Fibonacci is given with experimental values. It is shown that well-known conformity to law of development the information technologies is doubling of amount transistors on the integrated circuits during each 18 months, that is often named «Moore’s law» is the partial case of the generalized Fibonacci’s row. Offered correlations for the quantitative estimation of scale multiplier the rates of increase the system of q and his connection is set with a parameter γ. It has next physical maintenance: for the dynamics of populations γ characterizes the period of achievement a reproductive age females, and in the innovative economic systems is a period of "ripening" the innovations, their time of development from an idea – to the market. A list over of innovative advantages of development ІТ and production of electromobiles is brought, as one of the most dynamic industries of world economy. A promising direction for further research is the dissemination of the proposed approaches and the results obtained for forecasting the dynamics and development of solutions for managing the system of introduction of innovations into production.
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