APPLICATIONS OF CHAOS THEORY TO STATISTICAL MODELS

Abstract

Our research is based on the problem of substantiation of use of basic provisions of the chaos theory for local modeling of economic processes. Chaos theory represents a set of techniques for analyzing dynamical systems that are deterministic and yet very sensitive to perturbations of input. This theory is connected with mathematical catas-trophe theory, when a point in a model of an input-output system, where a vanishingly small change in the input can produce a large change in the output. In this article we examine mathematical catastrophe model on the example of the industrial enterprise PrJSC “Ukrgraphite” in relation to the development model, which allows us to draw a conclusion about the stable imbalance development of the enterprise. PrJSC “Ukrgraphite” produces carbon graphite products focusing on various branches of the metallurgical industry, namely: steelmaking, ferroalloy, aluminum, titanium-magnesium and others. Based on the analysis of the economic indicators of the enterprise PrJSC “Ukrgraphite”, we assessed its sustainability. If it is established that the relationship between the variables that characterize the behavior of the system is described by a polynomial of the third degree then it can be asserted that the system may exhibit insta-bility. In the paper we obtained the coefficients of the equation of the theory of catastrophe and we may concluded that the economic condition of PrJSC “Ukrgraphite” can be characterized as sustainable development. The practical appli-cation of the model enables to assess possible changes in the sustainability of the enterprise’s development under the influence of the determining evaluation criteria. The advantages of applying theory of chaos are that the ideas embed-ded in catastrophe theory help to understand the real experience of change management. In addition, one can see why real change is a dangerous phenomenon. The theory shows why changes cannot be “managed”, but they can be influ-enced.