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Asymptotic Behavior of Solutions of Equations of Main Resonance

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Abstract

We investigate a system of two first-order differential equations that appears when averaging nonlinear systems over fast one-frequency oscillations. The main result is the asymptotic behavior of a two-parameter family of solutions with an infinitely growing amplitude. In addition, we find the asymptotic behavior of another two-parameter family of solutions with a bounded amplitude. In particular, these results provide the key to understanding autoresonance as the phenomenon of a considerable growth of forced nonlinear oscillations initiated by a small external pumping.

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  1. Ufa Scientific Center, RAS, Mathematical Institute, Ufa, Russia

    L. A. Kalyakin

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  1. L. A. Kalyakin
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Kalyakin, L.A. Asymptotic Behavior of Solutions of Equations of Main Resonance. Theoretical and Mathematical Physics 137, 1476–1484 (2003). https://doi.org/10.1023/A:1026065025429

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