E. Menichellasaetta

Extraction of periodic signals from a noise background

Abstract A simple technique for extracting periodic signals from a noise background is proposed and tested. A selective amplifier circuit has been realized accordingly, which is capable of resolving low-frequency periodic components in short signal samples.

Thermally activated escape controlled by colored multiplicative noise

Abstract Thermally driven escape over a barrier which fluctuates with Gaussian statistics is studied by means of analog simulation. The phenomenon of resonant activation [C.R. Doering and J.C. Gadoua, Phys. Rev. Lett. 69 (1992) 2318] occurs when the correlation-time of the barrier fluctuations is increased without changing the amplitude. The dependence of the relevant escape time on the fluctuation variance exhibits a number of properties, independent of the potential shape, which eluded previous investigations.

Statistical properties of nonlinear systems driven by band-limited noise

Abstract Stochastic relaxation in a strongly nonlinear one-dimensional potential driven by band-limited noise is investigated by means of analogue simulation. On suitably high-pass filtering the stochastic process under study, intermittent bursts become observable. Most statistical properties related with this phenomenon appear to be universal, i.e. independent of the noise statistics, over a wide frequency range.

A new definition of stochastic resonance

SummaryStochastic resonance in a bistable potential is characterized as a syncronization effect of the hopping mechanism induced by the external periodic bias. Most notably, syncronization is shown i) to attain a maximum with increasing the forcing frequency close to the relevant switching rate, thus revealing abona fide resonant process; ii) to occur even in the absence of symmetry breaking by the periodic forcing term.

Intermittency in nonlinear stochastic systems

Abstract A nonlinear system driven by band-limited Gaussian noise is shown to exhibit intermittent dynamics. The existence of intermittent bursts is revealed by high-pass filtering the system response with cut-on frequency where the random force vanishes. The statistics of stationary intermittency, i.e. the amplitude and time distribution of the bursts, is determined in detail by analogue simulation of a simple monostable system, the quartic oscillator, in the limit of strong nonlinearity.

Escape rates in underdamped bistable potentials driven by coloured noise

Abstract The brownian motion in a quartic double-well potential driven by coloured noise is investigated in the low-viscosity limit by means of analogue simulation. The dependence of the escape rate on the noise correlation-time τ is determined for the conditions simulated: the escape rate decreases exponentially with increasing τ 2 . The relevant law is derived theoretically in the limit of vanishingly small viscosity and high potential barriers.

INTERMITTENCY DRIVEN BY BAND-LIMITED NOISE - THE INERTIAL REGIME

Nonlinear systems driven by band-limited noise exhibit intermittent dynamics over a wide frequency domain, as revealed by high-pass filtering the system response at a cut-on frequency much higher than the noise cut-off frequency. The statistics of the stationary intermittency thus developed is investigated in detail by analogue simulation of a simple monostable system, the overdamped quartic oscillator, in the limit of strong nonlinearity. The mathematical interpretation of our results is provided in terms of a statistically refined singular-perturbation argument, which explains the occurrence of an intermittent burst in the high-pass filtered signal with the close coincidence of a signal inflection point with a noise zero-crossing. Our interest focuses on a characteristic frequency domain, where the intermittent phenomenon is sensitive to the nonlinear nature of the system, only, irrespective of the driving noise statistics (inertial range).

Zero-crossing distributions for smoothed random signals

Abstract The classic problem of zero-crossings for smoothed random signals is revisited. Existing theoretical results and new predictions for the zero-crossing time distributions of Gaussian noises are checked by means of analogue simulation.

RESONANT CROSSING PROCESSES IN BISTABLE SYSTEMS

The crossing processes in an overdamped double‐well potential driven by an external colored noise and a weak sinusoidal time‐dependent modulation are investigated by means of analogue simulation. A new resonance phenomenon (resonant crossing) is revealed.

Stochastic Resonance in Bistable Systems with Fluctuating Barriers

A multiplicative bistable system perturbed by a periodic forcing term is shown to exhibit stochastic resonance with increasing the intensity of the multiplicative noise. Such an effect is related to the phenomenon of stochastic stabilization, which takes place in the unperturbed system.