Chaotic motion of a weakly nonlinear, modulated oscillator

A weakly nonlinear, weakly damped oscillator which is driven near resonance by a slowly modulated force is considered. This system models the combined effects of resonance, amplitude modulation, and nonlinearity. It may be described by a pair of first-order nonautonomous ordinary differential equations (ode) or, by regarding the modulation phase as a dependent variable, three autonomous ode, the smallest number of such equations (with regular excitation) which admits chaotic solutions. The oscillator is described by the Duffing equation. Attention is given to envelope-evolution equations, periodic solutions, numerical results, and a quasi-stationary solution.