An approach to logical-mathematical computer modeling of linear and nonlinear dynamical systems

Abstract

The paper deals with the problem of modeling linear and nonlinear dynamical systems using information technologies and programming. The processes of modeling, synthesis and inference of solutions to problems are considered, and the possibility of their integration within the described approach is shown. The substantive aspects of the development of special mathematical and algorithmic support for the construction of a software system for the analysis and processing of expert information for the purposes of automated synthesis and inference of solutions are briefly outlined. The aim of the work is to create a new approach of logical-mathematical computer modeling of linear and nonlinear dynamical systems and to develop a prototype of a software computational expert system based on it. As a result of the research, a universal approach of logical-mathematical computer modeling of linear and nonlinear dynamical systems has been developed and proposed. The proposed approach can be used to organize the process of computer modeling and automated synthesis of task solutions with the output of their results. The mathematical model of the knowledge base and process of its construction for the selected subject area, as well as the algorithm for outputting solutions to problems with its software implementation in the Python programming language, are shown. Examples of solution output for various linear and nonlinear problems are given. The developed prototype of the software computational expert system using the proposed logical- mathematical approach will significantly simplify the process of modeling dynamical systems and make the solution of problems' simpler and more understandable.