We consider the system of differential equations describing the initial step of capture of nonlinear oscillations in autoresonance under weak dissipation. We study the stability in probability of resonance solutions with unboundedly growing amplitude under persistent random perturbations. Bibliography: 11 titles. Illustrations: 1 Figure
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O. A. Sultanov, “Stability of autoresonance models subject to random perturbations for systems of nonlinear oscillation equations” [in Russian], Zh. Vych. Mat. Mat. Fiz. 54, No. 1, 65–79 (2014); English transl.: Computat. Math. Math. Phys. 54, No. 1, 59–73 (2014).
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Translated from Problemy Matematicheskogo Analiza 86, July 2016, pp. 87–93.
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Sultanov, O.A. Random Perturbations of Autoresonance in Oscillating Systems with Small Dissipation. J Math Sci 219, 267–274 (2016). https://doi.org/10.1007/s10958-016-3104-7