Generalized stochastic resonance in a linear fractional system with a random delay

Abstract

The generalized stochastic resonance (GSR) phenomena in a linear fractional random-delayed system driven by a weak periodic signal and an additive noise are considered in this paper. A random delay is considered for a linear fractional Langevin equation to describe the intercellular signal transmission and material exchange processes in ion channels. By virtue of the small delay approximation and Laplace transformation, the analytical expression for the amplitude of the first-order steady state moment is obtained. The simulation results show that the amplitude curves as functions of different system parameters behave non-monotonically and exhibit typical characteristics of GSR phenomena. Furthermore, a physical explanation for all the GSR phenomena is given and the cooperative effects of random delay and the fractional memory are also discussed.

Trichotomous noise induced stochastic resonance in a fractional oscillator with random damping and random frequency

“…These proteins undergo spontaneous conformational dynamics resulting in stochastic intermittent events of opening and closing of the pores [55]. Gao [56] proposed a linear fractional random-delayed oscillator with random frequency to investigate this phenomenon, and discussed the cooperative eects of random delay and the fractional memory on the generalized stochastic resonance (GSR). Usually, the damping and spring stiness are immersed in the same environment, and fluctuations in the damping and spring stiness can influence the dynamics of systems [45].…”