Abstract
We study the oscillator equations describing a type of nonlinear amplifier, exemplified by a two-junction superconducting quantum interference device. Just beyond the onset of spontaneous oscillations, the system is known to show significantly enhanced sensitivity to very weak magnetic signals. The global phase-space structure allows us to apply a center manifold technique to calculate the frequency of spontaneous oscillations as a function of the natural control parameters. The derived scaling form compares very well with numerical simulations. The ability to quantify the oscillation frequency permits its exploitation as a detection/analysis tool in remote sensing applications, and could also provide a pathway to a dynamic lowering of the low-frequency noise floor in oscillators exhibiting this class of dynamical behavior.
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