STUDY OF THE GEOMETRIC STRUCTURE OF PHASE PORTRAITS OF A NONLINEAR SYSTEM IN A PLANE

Tetiana Hnitetska; Halyna Hnitetska

doi:10.20535/ngikg2024.XIIІ.309773

STUDY OF THE GEOMETRIC STRUCTURE OF PHASE PORTRAITS OF A NONLINEAR SYSTEM IN A PLANE

Автор(и)

Tetiana Hnitetska National technical university of Ukraine "Kyiv Polytechnic Institute named after Igor Sikorsky" (Ukraine), Україна https://orcid.org/0000-0001-9682-6488
Halyna Hnitetska National technical university of Ukraine "Kyiv Polytechnic Institute named after Igor Sikorsky" (Ukraine), Україна https://orcid.org/0000-0002-2864-3142

DOI:

https://doi.org/10.20535/ngikg2024.XIIІ.309773

Ключові слова:

nonlinear dynamics, phase portraits, stability according to Lyapunov

Анотація

the article is devoted to the study of the mathematical model given by the system of nonlinear differential equations for the purpose of identifying its equilibrium points and conducting an analysis of the stability of these points in accordance with the Lyapunov stability method. The performed studies allow to provide a geometric interpretation of the behavior of the system and to visually present its phase portraits. Such an analysis makes it possible to predict the modes of operation of the system under different initial conditions. The research of the mathematical model is carried out by numerical methods in the MATLAB system for engineering and mathematical calculations using the integration of the system of differential equations by the Runge-Kut method of the 4th order

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Опубліковано

2024-08-22

Як цитувати

Hnitetska, T., & Hnitetska, H. (2024). STUDY OF THE GEOMETRIC STRUCTURE OF PHASE PORTRAITS OF A NONLINEAR SYSTEM IN A PLANE. Прикладна геометрія, інженерна графіка та об’єкти інтелектуальної власності, 1(XIIІ), 25–29. https://doi.org/10.20535/ngikg2024.XIIІ.309773