Title | Analysis of the scenario of limit cycle bifurcations phase system of differential equations |
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Authors | S. S. Mamonov^{1}, A. O. Kharlamova^{1}^{1}Рязанский государственный университет им. С. А. Есенина |

Annotation | The 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 |

Citation | Mamonov 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: 16.02.2019. |

**© SVMO, National Research Mordovia State University, 2019**

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