Geodesic
Stability of capture into parametric autoresonance
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 1, pp. 220-230

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A mathematical model describing the initial stage of a capture into parametric autoresonance in nonlinear oscillating systems is considered. The resonance corresponds to solutions with unboundedly growing energy. The stability of such solutions with respect to persistent perturbations on an asymptotically large time interval is investigated. A class of admissible perturbations is described for which a capture into parametric autoresonance occurs.
Keywords: parametric resonance; nonlinear oscillations; perturbations; stability. 
@article{TIMM_2015_21_1_a22,
     author = {O. A. Sultanov},
     title = {Stability of capture into parametric autoresonance},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {220--230},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2015_21_1_a22/}
}
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O. A. Sultanov. Stability of capture into parametric autoresonance. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 1, pp. 220-230. http://geodesic.mathdoc.fr/item/TIMM_2015_21_1_a22/