K. Flensberg et H. Svensmark, SCALING RELATIONS FOR FORCED OSCILLATORS AT THE TRANSITION FROM A DISSIPATIVE TO A HAMILTONIAN SYSTEM, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 47(3), 1993, pp. 2190-2192
The dynamics and the stability of a forced damped nonlinear oscillator
driven at twice its resonance frequency are studied. At the transitio
n from a dissipative system to a Hamiltonian system, simple scalings r
elations are found by the use of the Floquet theory of the linearized
problem. The Floquet exponents and the period-doubling bifurcation poi
nt are determined analytically in the limit of small damping. The theo
ry is compared to numerical calculations on a Duffing oscillator and e
xcellent agreement is found.