A comparative study of stochastic resonance for a model with two pathways by escape times, linear response, invariant measures and the conditional Kolmogorov-Smirnov Test

TL;DR

This paper investigates stochastic resonance in a two-pathway potential model, introducing new statistical detection methods including a conditional KS test, and analyzes how different measures detect resonance under various conditions.

Contribution

It introduces a new conditional Kolmogorov-Smirnov test for analyzing stochastic resonance and compares multiple detection measures in a two-pathway potential model.

Findings

Escape time distribution reveals stochastic resonance.

Conditional KS test reliably detects resonance.

Synchronization affects the detectability of resonance.

Abstract

We consider stochastic resonance for a diffusion with drift given by a potential, which has two metastable states and two pathways between them. Depending on the direction of the forcing, the height of the two barriers, one for each path, will either oscillate alternating or in synchronisation. We consider a simplified model given by a continuous time Markov Chains with two states. This was done for alternating and synchronised wells. The invariant measures are derived for both cases and shown to be constant for the synchronised case. A PDF for the escape time from an oscillatory potential is studied. Methods of detecting stochastic resonance are presented, which are linear response, signal-noise ratio, energy, out-of-phase measures, relative entropy and entropy. A new statistical test called the conditional Kolmogorov-Smirnov test is developed, which can be used to analyse stochastic resonance. An explicit two dimensional potential is introduced, the critical point structure derived and the dynamics, the invariant state and escape time studied numerically. The six measures are unable to detect the stochastic resonance in the case of synchronised saddles. The distribution of escape times however not only shows a clear sign of stochastic resonance, but changing the direction of the forcing from alternating to synchronised saddles an additional resonance at double the forcing frequency starts to appear. The conditional KS test reliably detects the stochastic resonance. This paper is mainly based on the thesis "Stochastic Resonance for a Model with Two Pathways"