Fractal Approach to Forming of Modified Bifurcation Diagrams in Practical Applications

Abstract

The points connected with both improving the methods based on the use of the bifurcation analysis and opening new possibilities to use the bifurcation analysis in practical applications are discussed in the paper. So, the fractal approach to form modified bifurcation diagrams is developed. Th e approach is directed towards extending knowledge about the nonlinear dynamics state-of-the-art by means of the growth in the capacity and adequacy of information about nonlinear dynamics regularities and uncertain ties. In particular, it is summarized the peculiarities of the fractal approach; it is signed the main ways to practical applications of the fractal approach – forecasting nonlinear dynamics, estimating the stability margin and risk.