Nonlinear Response With Dichotomous Noise

TL;DR

This paper investigates the effects of dichotomous noise on nonlinear systems, highlighting the need to modify standard analysis methods when unstable fixed points are involved, and provides analytic results for hypersensitive transport.

Contribution

It introduces modified calculation techniques for systems driven by dichotomous noise crossing unstable fixed points, with a focus on hypersensitive transport phenomena.

Findings

Standard results fail when unstable fixed points are crossed.

Modified calculations yield accurate long-term behavior.

Analytic results for hypersensitive transport are presented.

Abstract

Dichotomous noise appears in a wide variety of physical and mathematical models. It has escaped attention that the standard results for the long time properties cannot be applied when unstable fixed points are crossed in the asymptotic regime. We show how calculations have to be modified to deal with these cases and present as a first application full analytic results for hypersensitive transport.