Geodesic
Stability of autoresonance in dissipative systems
Ufa mathematical journal, Tome 7 (2015) no. 1, pp. 58-69

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We consider a mathematical model describing the initial stage of a capture into autoresonance in nonlinear oscillating systems with a dissipation. Solutions whose amplitude increases unboundedly in time correspond to a resonance. An asymptotic expansion for such solutions is constructed as a power series with constant coefficients. The stability of autoresonance with respect to persistent perturbations is studied by means of Lapunov's second method. We describe the classes of perturbations for which a capture into autoresonance occurs.
Keywords: resonance, nonlinear oscillations, dissipation, stability.
Mots-clés : perturbations 
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O. A. Sultanov. Stability of autoresonance in dissipative systems. Ufa mathematical journal, Tome 7 (2015) no. 1, pp. 58-69. http://geodesic.mathdoc.fr/item/UFA_2015_7_1_a5/