Relation between stochastic resonance and synchronization of passages in a double-well system

Abstract

We calculate, numerically, the residence times (and their distribution) of a Brownian particle in a two-well system under the action of a periodic, saw-tooth type, external field. We define hysteresis in the system. The hysteresis loop area is shown to be a good measure of synchronization of passages from one well to the other. We establish connection between this stochastic synchronization and stochastic resonance in the system.

Total entropy production fluctuation theorems in a nonequilibrium time-periodic steady state

“…Noise plays a constructive role in this case and SR finds applications in almost all areas of natural sciences. To characterize this resonance behaviour, different quantifiers have been introduced in the literature [39,40,41,42,43,44,45,46]. The work injected into the system (or the thermodynamic work done on the system) per cycle characterizes SR as a bona fide resonance [40,45,46].…”

Quantifying stochastic resonance: theory versus experiment

“…Considered as a function of the driving frequency , SNR and SPA exhibit a monotonic behaviour for typical systems of interest, while HLA still shows a resonance-type nonmonotonicity, referred to as bona fide SR. We remark that considered as functions of each of the three quantifiers completely fixes the other two thanks to the Kramers-Kronig relations (14) and (15) in combination with (24), (26) and (34).…”

“…Two prominent quantifiers of SR in such a case are based on residence time distributions [2-4, 9, 10] and hysteresis loop areas [11][12][13][14][15][16][17][18][19], as discussed in detail in sections 2-5. Our summary and conclusions are contained in section 6.…”

Energy fluctuations in a biharmonically driven nonlinear system

“…Around and beyond SR, pumping is quite small as shown in the inset of figure 2. Stochastic resonance being a synchronization phenomenon [30,33] it is expected that particle hopping dynamics between the wells get synchronized with the input signal. We find that the relative variance (RV) in physical quantities such as work = √…”

“…Because of its generic nature, this phenomenon boasts applications in almost all areas of natural science [28]. To characterize this resonance phenomenon, several different quantifiers have been introduced in the literature [28,29,30,31,32,33,34,35]. One of the quantifiers, namely the input energy of the system or the work done on the system per cycle is known to characterize SR as a bona fide resonance [24,25,34,35].…”