Noise effects in a nonlinear dynamic system: The rf superconducting quantum interference device

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Abstract
We consider the rf superconducting quantum interference device above its homoclinic threshold. The effects of weak additive (i.e., Langevin) noise on the dynamics of the system are analyzed from the standpoint of the effects on the chaotic attractors and the maximal Liapunov exponents that characterize the system in this regime. It is seen that noise has a ‘‘smoothing’’ effect on chaotic attractors. On the other hand, the injection of noise can lead to a change in sign of the Liapunov exponent that characterizes a periodic point in its absence, leading to ‘‘noise-induced chaos.’’ We also consider the cases of additive fluctuations that manifest themselves as a fluctuating dc driving term, and multiplicative fluctuations (at initial times) in the nonlinearity parameter. In these cases, we study the motion of the system, in the mean, by averaging over numerous realizations of the fluctuating driving term. Depending on the strength of the fluctuations, one obtains mixtures of periodic and chaotic motion in the multiplicative-noise case.

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