Coherence resonance in subdiffusive fractional Klein-Kramers periodic potential systems without a bifurcation precursor

Abstract

Coherence resonance of normal diffusive and subdiffusive Brownian particles moving within a static periodic potential is investigated by the method of moments through the dissipationfluctuation relation. It is shown that coherence resonance could happen in the background of both normal diffusion and subdiffusion. The importance of the current investigation is twofold; on the one hand, it generalizes coherence resonance to a model which surpasses the limitation of either of the two commonly accepted requisites and, on the other hand, it demonstrates subdiffusion has an inhibitory effect on coherence resonance in the system under study.

Mean First Passage Time and Stochastic Resonance in a Transcriptional Regulatory System with Non-Gaussian Noise

“…Within a linear response range [25][26][27][28], we seek the long term solution of Eq. (27) in the form p (as) where p i0 and p i1 (i − 1, 2) are coefficients to be determined.…”

“…Our purpose is to analytically deduce the MFPTs of a gene transcriptional regulatory system driven by non-Gaussian noise. As an application of the derived MFPTs, we further explore the effect of non-Gaussian noise on SR based on a new combination of adiabatic elimination [6,21,22] and linear response approximation [23][24][25][26][27][28].…”

Stochastic Resonance and Bifurcation of Order Parameter in a Coupled System of Underdamped Duffing Oscillators

“…Next, take t t   cos ) ( 0   with 1 0   to calculate the linear susceptibility. The main idea underlying the calculating procedure is to combine the method of weighed series expansion [Evstigneev et al, 2002;Kang et al, 2003;Kang, 2011;Liu & Kang, 2018] and the harmonic balance method [Lim et al, 2001], where the weighting function is taken as the stationary solution of the unperturbed version of Eq. (3) so as to satisfy the natural boundary conditions.…”

“…(3) so as to satisfy the natural boundary conditions. This method was applied to linear FP equations before [Evstigneev et al, 2002;Kang et al, 2003;Kang, 2011;Liu & Kang, 2018], but it is applied to the nonlinear FP equation here for the first time.…”

“…In order to find ) , ( Here, it is remarked that the decomposition with respect to the velocity v is the same as that in [Evstigneev et al, 2002;Liu & Kang, 2018], but a bit different from that in [Kang et al, 2003;Kang, 2011]. Nevertheless, numerical experiment shows that the two forms of decomposition have the same convergence speed.…”