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Asymptotic Solution of the Autoresonance Problem

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Abstract

We study the problem of forced oscillations near a stable equilibrium of a two-dimensional nonlinear Hamiltonian system of equations. A given exciting force is represented as rapid oscillations with a small amplitude and a slowly varying frequency. We study the conditions under which such a perturbation makes the phase trajectory of the system recede from the original equilibrium point to a distance of the order of unity. To study the problem, we construct asymptotic solutions using a small amplitude parameter. We present the solution for not-too-small values of time outside the original boundary layer.

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  1. Ufa Scientific Center, Institute of Mathematics, RAS, Ufa, Russia

    L. A. Kalyakin

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  1. L. A. Kalyakin
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Kalyakin, L.A. Asymptotic Solution of the Autoresonance Problem. Theoretical and Mathematical Physics 133, 1684–1691 (2002). https://doi.org/10.1023/A:1021318426151

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