Universality of zero-dispersion peaks in the fluctuation spectra of underdamped nonlinear oscillators

Zero-dispersion peaks (ZDP's), which can arise in the fluctuation spectra of noise-driven underdamped oscillators for which the dependence of the eigenfrequency $\omega \mathrm{}\left(E\right)\mathrm{}$ on energy $E$ possesses a maximum or minimum, have been investigated by means of analog electronic experiments. Two different model systems were studied: a tilted Duffing oscillator and a model of a bistable superconducting quantum-interference device (SQUID). It is demonstrated experimentally that, for strong enough intensity $T$ of Gaussian pseudowhite noise (equivalent to temperature in a thermal system), the shape of a ZDP becomes universal, independent of the system under investigation. Its evolution with $T$ is also shown to exhibit universal features, being governed by a single parameter provided that $T$ exceeds a critical value $T_c$, below which the ZDP disappears abruptly. The hierarchy of universalities connected to particular types of extrema in $\omega \mathrm{}\left(E\right)\mathrm{}$ is discussed. The results are of relevance to underdamped SQUID's and, in particular, to the recently discovered phenomenon of zero-dispersion stochastic resonance.