Lazarenko S. Methods of analyzing of nonlinear discrete anticipatory systems

Lazarenko S.V. Methods of analyzing of nonlinear discrete anticipatory systems. – Manuscript. The thesis for the degree of Candidate of Physical and Mathematical Sciences on the specialty 01.05.04 – Systems Analysis and Theory of Optimal Solutions. – National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Ministry of Education and Science of Ukraine Kiev, 2019. The thesis is devoted to the generalization of mathematical and the development of software tools for analysis of discrete nonlinear systems with anticipations (AS). The parameter space of a discrete nonlinear system with strong first-order antisipation is investigated. Their boundary sets are investigated for fractal properties. The symbolic dynamics apparatus obtained relations for estimating the Hausdorff dimension on top of boundary sets of dynamical systems with a multivalued evolution operator in which nonlinear selectors do not intersect, and for the partial case with self-intersections. The uniqueness and the necessary condition for the existence of a solution of the proper relation for the case of self-intersections is proved. Methods for constructing dynamic modes maps and the senior Lyapunov index for systems with multivalued evolution operators with reduction of time computational complexity are generalized. Spatio-temporal computational complexities of their modeling are obtained and presented, and their representation of their states by multisets is proposed, to minimize these computational costs. Keywords: time-advance systems, dynamic system, fractal dimension, Lyapunov exponents, Hutchinson operator, multi-valued maps, symbolic dynamics, computation complexity.