A Study on Stochastic Resonance in Biased Subdiffusive Smoluchowski Systems within Linear Response Range

Abstract

The method of matrix continued fraction is used to investigate stochastic resonance (SR) in the biased subdiffusive Smoluchowski system within linear response range. Numerical results of linear dynamic susceptibility and spectral amplification factor are presented and discussed in two-well potential and mono-well potential with different subdiffusion exponents. Following our observation, the introduction of a bias in the potential weakens the SR effect in the subdiffusive system just as in the normal diffusive case. Our observation also discloses that the subdiffusion inhibits the low-frequency SR, but it enhances the high-frequency SR in the biased Smoluchowski system, which should reflect a “flattening" influence of the subdiffusion on the linear susceptibility.

Effect of spatial correlation on stochastic resonance in two linearly interacting noisy bistable oscillators

“…Due to the spatial nonlinearity and the temporal nonhomogeneity, there is normally no analytic or numerical technique which can calculate the response of general stochastic resonant systems apart from bistable systems. For a single standard or biased overdamped bistable system, several theoretical methods, including two-state theory [14]- [16], linear response approximation [17]- [20], matrix continuation fraction [21]- [23], eigenfunction perturbation [24,25], and the method of moments [26]- [28], have been developed to explore SR within or beyond the linear response range. Among these methods, the linear response approximation and the method of moments have been extended to uncoupled bistable arrays [29] and mean-field coupled bistable arrays [30], respectively; however, the effect of correlation of the internal noise of the consisting elements has not been taken into account in these extensions.…”