Study of forced oscillations of a chain of three coupled oscillators near resonance

Title	Study of forced oscillations of a chain of three coupled oscillators near resonance
Authors	P. A. Shamanaev¹, D. A. Katin¹, N. V. Oshina¹ ¹National 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: 16.10.2024.