Information Length as a New Diagnostic of Stochastic Resonance

Stochastic resonance is a subtle, yet powerful phenomenon in which a noise plays an interesting role of amplifying a signal instead of attenuating it. It has attracted a great attention with a vast number of applications in physics, chemistry, biology, etc. Popular measures to study stochastic resonance include signal-to-noise ratios, residence time distributions, and different information theoretic measures. Here, we show that the information length provides a novel method to capture stochastic resonance. The information length measures the total number of statistically different states along the path of a system. Specifically, we consider the classical double-well model of stochastic resonance in which a particle in a potential V (x, t) = [−x2/2 + x4/4 − A sin(ωt) x] is subject to an additional stochastic forcing that causes it to occasionally jump between the two wells at x≈ ±1. We present direct numerical solutions of the Fokker-Planck equation for the probability density function p(x, t), for ω = 10−2 to 10−6, and A ∈ [0,0.2] and show that the information length shows a very
clear signal of the resonance. That is, stochastic resonance is reflected in the total number of different statistical states that a system passes through.