Autoresonance in oscillating systems with combined excitation and weak dissipation

A mathematical model describing the initial stage of capture into autoresonance for nonlinear oscillating systems with combined parametric and external excitation is considered. The solutions unboundedly growing amplitude limited phase mismatch correspond to autoresonant capture. paper investigates existence, stability bifurcations such in presence a weak dissipation system. Our technique based on study particular power-law asymptotics at infinity construction suitable Lyapunov functions.