Logical stochastic resonance in bistable system under α-stable noise

Abstract

In the presence of α-stable noise, the logical stochastic resonance (LSR) phenomenon in a class of double well nonlinear system is investigated in this paper. LSR effect is obtained under α-stable noise. The probability of getting correct logic outputs is used to evaluate LSR behavior. Four main results are presented. Firstly, in the optimal band of noise intensity, Gaussian white noise is considered a better choice than heavy tailed noise to obtain clean logic operation. But at weak noise background, the success probability of getting the right logic outputs is higher when the system is subjected to heavy tailed noise. Secondly, it is shown that over the entire range of noise variance, the asymmetric noise induced LSR performs better than that induced by the symmetric noise. Furthermore, we find which side the tail skews also affects the correct probability of LSR. At last, the fractional Fokker-Planck equation is presented to show when the characteristic exponent of α-stable noise is less than 1, LSR behavior will not be obtained irrespective of the setting for other parameters.