Information Length as a New Diagnostic of Stochastic Resonance†

Abstract

Stochastic resonance is a subtle, yet powerful phenomenon in which noise plays an interesting role of amplifying a signal instead of attenuating it. It has attracted 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 ) = [ - x 2 / 2 + x 4 / 4 - A sin ( ω t ) 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.