Chaotic motion of a weakly nonlinear, modulated oscillator
AUTOR(ES)
Miles, John
RESUMO
A weakly nonlinear oscillator of natural frequency ω0 and damping ratio δ is driven by an amplitude-modulated force of dimensionless amplitude ε, carrier frequency ω, and modulation frequency ω1. Each of (ω - ω0)/ω0, ω1/ω0, and δ is O(ε2/3) as ε → 0. The response in this resonant neighborhood is a slowly modulated sine wave, the envelope of which is described by three first-order, autonomous, ordinary differential equations. This envelope, which is periodic for δ >> ε2/3, is chaotic in certain ranges of (ω - ω0)/ω0 and ω1/ω0 if δ/ε2/3 is sufficiently small.
