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Article

Fischer, Cyril ; Náprstek, Jiří
Identification of quasiperiodic processes in the vicinity of the resonance. (English). In: Chleboun, J., Kůs, P., Papež, J., Rozložník, M., Segeth, K. and Šístek, J. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Jablonec nad Nisou, June 19-24, 2022. Institute of Mathematics CAS, Prague, 2023. pp. 57-64
MSC: 34A12, 37C60, 37N05, 70G60 | DOI: 10.21136/panm.2022.06
Keywords:
dynamical systems; quasiperiodic response; van der Pol equation
Summary:
In nonlinear dynamical systems, strong quasiperiodic beating effects appear due to combination of self-excited and forced vibration. The presence of symmetric or asymmetric beatings indicates an exchange of energy between individual degrees of freedom of the model or by multiple close dominant frequencies. This effect is illustrated by the case of the van der Pol equation in the vicinity of resonance. The approximate analysis of these nonlinear effects uses the harmonic balance method and the multiple scale method.
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