Geodesic
Autoresonant asymptotics in an~oscillating system with weak dissipation
Teoretičeskaâ i matematičeskaâ fizika, Tome 160 (2009) no. 1, pp. 102-111

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We study a system of two first-order differential equations arising in averaging nonlinear systems over fast single-frequency oscillations. We consider the situation where the original system contains weak dissipative terms. We construct the asymptotic form of a two-parameter solution with an unbounded increasing amplitude. This result gives a key for understanding autoresonance in weak dissipative systems as a phenomenon of significant increase in the forced nonlinear oscillation initiated by a small external pumping.
Keywords: nonlinear equation, small parameter, asymptotic behavior, resonance, dissipation.
Mots-clés : perturbation 
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     author = {L. A. Kalyakin and M. A. Shamsutdinov},
     title = {Autoresonant asymptotics in an~oscillating system with weak dissipation},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2009_160_1_a9/}
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L. A. Kalyakin; M. A. Shamsutdinov. Autoresonant asymptotics in an~oscillating system with weak dissipation. Teoretičeskaâ i matematičeskaâ fizika, Tome 160 (2009) no. 1, pp. 102-111. http://geodesic.mathdoc.fr/item/TMF_2009_160_1_a9/