Computer simulation of dynamic systems elements in Python

OBJECTIVE. Investigation of the possibilities of using the Python programming system in the analysis of processes in linear and nonlinear dynamic systems. t is often necessary to solve the problem of choosing modeling tools when creating and researching computer models METHOD The catastrophe method which takes into account abrupt changes arising in the form of a sudden response of the system to a smooth change in external conditions have been used in solving the set tasks. RESULTS The paper presents the results of testing the Python programming system as a basis for the development of computer models of linear and nonlinear dynamic systems. A brief description of the Python libraries and modules used in the development of systems described by differential equations and transfer functions is given. A theoretical review of the occurrence of chaotic processes in nonlinear dynamical systems is given, the mechanism of transition to chaos is demonstrated on the example of constructing a model based on the Verhulst equation. A mathematical model of the Lorentz equations is implemented, which describes the variety of chaotic changes in a nonlinear dynamic system, phase portraits of the model's output parameters are built in the form of three-dimensional graphs. It is concluded that the Python programming system can be used as a toolkit in the development of computer models of linear and nonlinear dynamic systems. The approbation of this approach have been carried out in the development of models of dynamic systems in the course of mathematical modeling of complex systems.