Injection locking near a stochastic bifurcation: the dc SQUID as a case study

We examine the response of a 2D nonlinear oscillator (exemplified in this work by the two-junction superconducting quantum interference device - SQUID) subject to a weak time-periodic target signal, just past the onset of a saddle-node bifurcation. Adjusting the control parameters of the device allows us to identify a regime wherein the response (characterized by an output signal-to-noise ratio at the target frequency) is maximal. The phenomenon has the flavor of the well-studied stochastic resonance effect but is, in fact, shown to arise from a nonlinear deterministic resonance in the “running solution” regime. Our results are presented in the context of experimental results.