Zalevska O. Geometric modeling for nonlinear dynamics process of fractal approximation method

The object of the study are processes developed on the laws of nonlinear dynamics. The method is based on the fractal dimension of the objects that characterize the stage of dynamic processes. There aim of the study the method to approximate structures formed by the flow of the nonlinear dynamic process by deterministic fractal is developed which provides the ability to track qualitative changes under the external factors' influence. Geometric modeling by fractal approximation method developed in the thesis extends the capabilities of the technological and physical processes' design and research. The following scientific results were obtained: the method for analyzing the geometric phase portraits of structures close to the fractal is developed; the law of development of the nonlinear process for the different physical and biological processes is investigated; the process of transition from chaos to order, and vice versa in nonlinear systems is studied; Fibonacci pattern is found with the fractal dimension in the study of the critical points of transients; changing dynamic structure in the position close to the steady with the base of the triangle; the fractal approximation of nonlinear processes similar to steady ones is developed with deterministic fractal for the mathematical description of the process with the specified accuracy. The study's results are introduced in medical practice in the design of the computer room for the doctor's preliminary analysis for stage of the disease and treatments, and used in the educational process at the NTUU "KPI".