Saint Petersburg, St. Petersburg, Russian Federation
Russian Federation
The study of dynamic systems (DS) on the phase plane is one of the common methods of oscillation theory and is widely used in engineering and scientific practice. Purpose: a combination of analytical research with computer simulation. Results: the article proposes and discusses a computational and graphical work on the subject "Systems Modeling," which is taught at a number of universities across the Russia. The practical significance lies in the use study of DS fosters intellectual development, creativity, and the development of professional competencies, thereby increasing the motivation of active students for research activities.
dynamic system on a plane, phase portraits, analytically-numerical study
1. Morozov A. V., Brigadnov I. A. Matematicheskie osnovy teorii sistem: dinamicheskie sistemy. SPb.: Severo-Zapadnyy gosudarstvennyy zaochnyy tehnicheskiy universitet, 2006. 214 s.
2. Morozov A. D., Dragunov T. N. Vizualizaciya i analiz invariantnyh mnozhestv dinamicheskih sistem. M.; Izhevsk: Institut komp'yuternyh issledovaniy, 2003. 304 s.
3. Bulekbaev D. A., Morozov A. V. Chislennoe issledovanie attraktorov v nestacionarnom uravnenii Duffinga // Perspektivy nauki. 2024. № 8 (179). S. 32–38.
4. Trenogin V. A. Obyknovennye differencial'nye uravneniya. M.: Fizmatlit, 2009. 312 s.
5. Arnol'd V. I. Geometricheskie metody v teorii obyknovennyh differencial'nyh uravneniy. 4-e izd. M.: MCNMO, 2012. 384 s.
6. Anosov D. V. Differencial'nye uravneniya: to reshaem, to risuem. 3-e izd., ster. M.: MCNMO, 2016. 200 s.
7. Morozov A. V. Kachestvennaya teoriya differencial'nyh uravneniy — osnovnaya sostavlyayuschaya teorii dinamicheskih sistem // Trudy Voenno-kosmicheskoy akademii imeni A. F. Mozhayskogo. 2014. Vyp. 642. S. 177–184.
8. Haken G. Sinergetika: ierarhii neustoychivostey v samoorganizuyuschihsya sistemah i ustroystvah / per. s angl. Yu. A. Danilova; pod red. Yu. L. Klimontovicha. M.: Mir, 1985. 419 s.
9. Ueda Y. Steady Motions Exhibited by Duffing’s Equation: A Picture Book of Regular and Chaotic Motions // New Approaches to Nonlinear Problems in Dynamics / P. J. Holmes (ed.). Philadelphia (PA): Society for Industrial and Applied Mathematics, 1980. Pp. 311–322.
10. Filippov A. F. Vvedenie v teoriyu differencial'nyh uravneniy: uchebnik. 2-e izd., ispr. M.: KomKniga, 2007. 240 s.
11. Montagnier P., Paige C. C., Spiteri R. J. Real Floquet Factors of Linear Time-Periodic Systems // Systems and Control Letters. 2003. Vol. 50, iss. 4. Pp. 251–262. DOI:https://doi.org/10.1016/S0167-6911(03)00158-0
12. Oka T., Kitamura S. Floquet Engineering of Quantum Materials // Annual Review of Condensed Matter Physics. 2019. Vol. 10. Pp. 387–408. DOI:https://doi.org/10.1146/annurev-conmatphys-031218-013423



