Resonant crossing processes controlled by colored noise

Nonlinear sensors: an approach to the residence time detection strategy

The monitoring of the residence time difference in bistable sensors has been recently proposed as a valid scheme for improving the detection capabilities of sensors as diverse as fluxgate magnetometers, ferroelectric sensors and mechanical sensors. In this paper we propose an approach to the residence time based detection strategy based on the measurement of the slope m of the sensor output integral. We demonstrate that such a method, far from degrading the detection performances can provide an easier way to realize fast and reliable sensors without the computationally demanding task related with the computation of the residence time difference. We introduce the receiver operating characteristic curve as a quantitative estimator for the comparison of the two methods and show that the detector performances increase with increasing the periodic bias amplitude A up to a maximum value. This condition has potentially relevant consequences in the future detectors design.

Noise sensitivity of phase-synchronization time in stochastic resonance: theory and experiment

Recent numerical and heuristic arguments have revealed that the average phase-synchronization time between the input and the output associated with stochastic resonance is highly sensitive to noise variation. In particular there is evidence that this average time exhibits a cusplike behavior as the noise strength varies through the optimal value. Here we present an explicit formula for the average phase-synchronization time in terms of the phase diffusion coefficient and the average frequency difference between the input and the output signals. We also provide experimental evidence for the cusplike behavior by using a bistable microelectronic-circuit system.

Noise-induced coherence in bistable systems with multiple time delays

We study the correlation properties of noise-driven bistable systems with multiple time-delay feedbacks. For small noisy perturbation and feedback magnitude, we derive the autocorrelation function and the power spectrum based on the two-state model with transition rates depending on the earlier states of the system. A comparison between the single and double time delays reveals that the auto correlation functions exhibit exponential decay with small undulation for the double time delays, in contrast with the remarkable oscillatory behavior at small time lags for the single time delay.

Residual aperiodic stochastic resonance in a bistable dynamic system transmitting a suprathreshold binary signal

Conventional stochastic resonance can be viewed as an amplitude effect, in which a small (subthreshold) input signal receives assistance from noise to trigger a stronger response from a nonlinear system. We demonstrate another mechanism of improvement by the noise, which is more of a temporal effect. An intrinsically slow system has difficulty to respond to a fast (suprathreshold) input, and the noise plays a constructive role by spurring the system for a more efficient response. The possibility of this form of stochastic resonance is established and studied here in a double-well bistable dynamic system, driven by a suprathreshold random binary signal, with the noise accelerating the switching between wells.

Coherence enhancement in nonlinear systems subject to multiplicative Ornstein-Uhlenbeck noise

We show that for two biologically relevant models with self-sustained oscillations under the action of a multiplicative Ornstein-Uhlenbeck process, their coherence response behaves nonmonotonically with the process correlation time. There is a correlation time for which the quality factor is optimized. This phenomenon is a consequence of the interplay between the correlation time and the system's periodicity. This relation is evidenced through a power law relation with an exponent close to -1 / 2.

Stochastic resonance and the benefits of noise: from ice ages to crayfish and SQUIDs

Noise in dynamical systems is usually considered a nuisance. But in certain nonlinear systems, including electronic circuits and biological sensory apparatus, the presence of noise can in fact enhance the detection of weak signals. This phenomenon, called stochastic resonance, may find useful application in physical, technological and biomedical contexts.