Title | Study of forced oscillations of a chain of three coupled oscillators near resonance |
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Authors | P. A. Shamanaev^{1}, D. A. Katin^{1}, N. V. Oshina^{1}^{1}National Research Mordovia State University |

Annotation | The Lyapunov-Schmidt method is used to study a mathematical model of oscillations in a chain of three coupled oscillators near a resonance with a small parameter, provided that the system is acted upon by an external periodic force with two commensurate frequencies. The algorithm developed based on the Lyapunov- Schmidt method is implemented in the SymPy Python mathematical library. An example is given that shows that if the parameters of a small perturbation are selected in a special way, then the solution components of the perturbed system have a pole at the point varepsilon = 0. |

Keywords | chain of coupled oscillators, forced oscillations, periodic solutions, small parameter, Lyapunov-Schmidt method, resonance. |

Citation | Shamanaev P. A., Katin D. A., Oshina N. V. ''Study of forced oscillations of a chain of three coupled oscillators near resonance'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, July 26-28, 2024). Saransk: SVMO Publ, 2024. - pp. 212-216. Available at: https://conf.svmo.ru/files/2024/papers/paper41.pdf. - Date of access: 12.11.2024. |

**© SVMO, National Research Mordovia State University, 2024**

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