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Emission of autoresonant trajectories and thresholds of resonant pumping (1802.06717v1)
Published 19 Feb 2018 in nlin.CD, math-ph, math.DS, and math.MP
Abstract: We study an autoresonant asymptotic behaviour for nonlinear oscillators under slowly changing frequency and amplitude of external driver. As a result we obtain formulas for threshold values of amplitude and frequency of the driver when autoresonant behaviour for the nonlinear oscillator is observed. Also we study a capture into resonance and emission out of the resonance for trajectories of the oscillator. A measure of autoresonant asymptotic behaviours for nonlinear oscillator is obtained.