Geodesic
Stability of autoresonance models subject to random perturbations for systems of nonlinear oscillation equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 1, pp. 65-79 
O. A. Sultanov. Stability of autoresonance models subject to random perturbations for systems of nonlinear oscillation equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 1, pp. 65-79. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_1_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Systems of differential equations arising in the theory of nonlinear oscillations in resonance-related problems are considered. Of special interest are solutions whose amplitude increases without bound with time. Specifically, such solutions correspond to autoresonance. The stability of autoresonance solutions with respect to random perturbations is analyzed. The classes of admissible perturbations are described. The results rely on information on Lyapunov functions for the unperturbed equations.

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