Stochastic dynamics in a two-dimensional oscillator near a saddle-node bifurcation - art. no. 066114

We study the oscillator equations describing a particular class of nonlinea r amplifier, exemplified in this work by a two-junction superconducting qua ntum interference device. This class of dynamic system is described by a po tential energy function that can admit minima (corresponding to stable solu tions of the dynamic equations), or "running states" wherein the system is biased so that the potential minima disappear and the solutions display spo ntaneous oscillations. Just beyond the onset of the spontaneous oscillation s, the system is known to show significantly enhanced sensitivity to very w eak magnetic signals. The global phase space structure allows us to apply a center manifold technique to approximate analytically the oscillatory beha vior just past the (saddle-node) bifurcation and compute the oscillation pe riod, which obeys standard scaling laws. In this regime. the dynamics can b e represented by an "integrate-fire" model drawn from the computational neu roscience repertoire: in fact, we obtain an "interspike interval'' probabil ity density function and an associated power spectral density (computed via Renewal theory) that agree very well with the results obtained via numeric al simulations. Notably, driving the system with one or more time sinusoids produces a noise-lowering injection locking effect and/or heterodyning.