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TMF, 2018, Volume 194, Number 3, Pages 385–402 (Mi tmf9375)  

Resonance capture in a system of two oscillators near equilibrium

L. A. Kalyakin

Institute of Mathematics with Computing Center, RAS, Ufa, Russia

Abstract: We consider a system of differential equations describing the interaction of two weakly coupled nonlinear oscillators. We assume that one oscillator is initially far from equilibrium, the other is near equilibrium, and their frequencies are close. We study the effect of resonance capture, when the frequencies of the coupled oscillators remain close while the oscillation energies change in time significantly; in particular, the second oscillator goes far from equilibrium. We find that the initial stage of resonance capture is described by the second Painlevé equation. We obtain such a description in the asymptotic approximation in a small parameter corresponding to the coupling constant.

Keywords: nonlinear oscillation, small parameter, asymptotic approximation, resonance capture.

Funding Agency Grant Number
Russian Science Foundation 17-11-01004
This research is supported by a grant from the Russian Science Foundation (Project No. 17-11-01004).


DOI: https://doi.org/10.4213/tmf9375

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English version:
Theoretical and Mathematical Physics, 2018, 194:3, 331–346

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Document Type: Article
Received: 29.03.2017

Citation: L. A. Kalyakin, “Resonance capture in a system of two oscillators near equilibrium”, TMF, 194:3 (2018), 385–402; Theoret. and Math. Phys., 194:3 (2018), 331–346

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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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