Aperiodic stochastic resonance in excitable systems

Abstract

Stochastic resonance (SR) is a phenomenon wherein the response of a nonlinear system to a weak periodic input signal is optimized by the presence of a particular level of noise. Here we present a new method and theory for characterizing SR-type behavior in excitable systems with aperiodic inputs. These novel developments demonstrate that noise can serve to enhance the response of a nonlinear system to a weak input signal, regardless of whether the signal is periodic or aperiodic.

Emergent global oscillations in heterogeneous excitable media: The example of pancreaticβcells

“…A periodically forced van der Pol-FitzHugh-Nagumo element shows behavior similar to a driven oscillator: phase locking, quasiperiodicity, period doubling, and chaos [34]. A quiescent excitable element may be excited by driving with a combination of a periodic subthreshold signal plus noise [35] or with an aperiodic subthreshold signal plus noise [36], phenomena which have been termed stochastic resonance, or with noise alone [37], when the phenomenon has been termed coherence resonance. Here, we have seen that even without any external forcing, either periodic or stochastic, a heterogeneous excitable medium can become self-excited to produce global oscillations.…”

Noise-sensitive measure for stochastic resonance in biological oscillators

“…A general feature associated with existing measures for characterization of SR is that either they vary slowly with noise about the optimal value, exhibiting a "bell-shape" behavior as typically seen in the SNR, or they are insensitive to noise variation (e.g., the correlation measure in the case of ASR [17,18,19]). Because of the ubiquity of SR in biological systems [4,5,6,7,8,9,10], a natural question is how a biological oscillator tunes to the optimal noise level to realize SR. For this purpose a measure that is highly sensitive to noise variation is desired.…”

“…There are also nonlinear systems, in particular excitable systems, for which the performance optimization can occur in a range of the noise level. This is referred to as aperiodic stochastic resonance (ASR) [17,18,19].…”

“…For an aperiodic signal, there may be no well-defined peaks in the Fourier spectrum. In this case, the correlation between the input and the output signal [17,18,19], entropies, and other quantities derived from the information theory [20,21,22,23,24,25] can be used for characterization, where SR means the optimization of such a measure by noise. There are also nonlinear systems, in particular excitable systems, for which the performance optimization can occur in a range of the noise level.…”

“…To explain the numerical finding (Sec. 3), we shall use the theoretical approach in references [17,18,19] in the study of ASR to reduce the system of FHN oscillators to a minimal model (Sec. 3.1): the double-well potential system that has been a paradigm to address many fundamental issues in SR.…”