Scaling relations for forced oscillators in the transition from a dissipative to a Hamiltonian system
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The dynamics and the stability of a forced damped nonlinear oscillator driven at twice its resonance frequency is studied. At the transition from a dissipative system to a Hamiltonian system, simple scalings relations are found by the use of the Floquet theory of the linearized problem. The Floquet exponents and the period-doubling bifurcation point are determined analytically in the limit of small damping. The theory is compared to numerical calculations on a Duffing oscillator and excellent agreement is found.
|Journal||Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)|
|Number of pages||3|
|Publication status||Published - 1 Mar 1993|