2015/02/28 by Oskar A. Sultanov, Oskar Sultanov, Sultanov, Oskar
Computer Science · Mathematics · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Quantum chaos and dynamical systems #math-ph #math.CA #math.MP
paper · pdf · doi:10.48550/arxiv.1503.00148
11 pages, 3 figures
arxiv created 2015/02/28 · arxiv updated 2015/03/03
A mathematical model describing the initial stage of the capture into the parametric autoresonance in nonlinear oscillating systems with a dissipation is considered. Solutions with unboundedly growing energy in time at infinity are associated with the autoresonance phenomenon. Stability of such solutions is investigated. We describe classes of admissible deterministic and random perturbations such that the stability of autoresonance is preserved on an asymptotically large interval.