Theoretical description of logical stochastic resonance and its enhancement: Fast Fourier transform filtering method.

Over the past decade, dynamic schemes have been proposed for the use of bistable systems in the design of logic devices. A bistable system in a noisy background can operate as a reliable logic gate in a moderate noise level, which is called a logical stochastic resonance (LSR). In this paper, we theoretically explore the emergence of LSR in general bistable systems and identify the dynamical mechanisms of LSR. The timescale relationship between the measured time and the mean first-pass time of two-state transitions is a key condition in determining whether the system is reliable. Furthermore, we demonstrate that the stability of the logic operation can be significantly improved by choosing the appropriate filtering method. Low-pass filtered noise-driven systems are more stable than Gaussian white noise. However, band-pass and high-pass filtered noise are harmful to the stability of the system due to the filtering of low-frequency components. Our theoretical and numerical simulation results offer perspectives for the development of logic devices.