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Analysis of the scenario of limit cycle bifurcations phase system of differential equations

TitleAnalysis of the scenario of limit cycle bifurcations phase system of differential equations
AuthorsS. S. Mamonov1, A. O. Kharlamova1
1Рязанский государственный университет им. С. А. Есенина
AnnotationThe article deals with a system of differential equations with a cylindrical phase space. For it, using the torus principle, conditions for the existence of limit cycles of the first kind are formulated. For the considered system, a numerical analysis of the scenario of bifurcations of a stable limit cycle is performed depending on the parameters of the system. The question of the number and methods of detection of unstable cycles arising as a result of bifurcation is considered.
Keywords system of differential equations, torus principle, limit cycle of the first kind, bifurcation, unstable cycle
CitationMamonov S. S., Kharlamova A. O. ''Analysis of the scenario of limit cycle bifurcations phase system of differential equations '' [Electronic resource]. Proceedings of the XIII International scientific conference ''Differential equations and their applications in mathematical modeling''. (Saransk, July 12-16, 2017). Saransk: SVMO Publ, 2017. - pp. 75-79. Available at: http://conf.svmo.ru/files/deamm2017/papers/paper10.pdf. - Date of access: 09.12.2019.