Phase Reduction in the Noise Induced Escape Problem for Systems close to Reversibility

TL;DR

This paper demonstrates that for near-reversible systems with stable stationary curves, the complex noise-induced escape problem can be effectively reduced to a one-dimensional analysis, simplifying the computation of quasipotentials.

Contribution

It introduces a reduction method for the noise-induced escape problem in near-reversible systems, approximating quasipotentials via restricted dynamics on stable curves.

Findings

The quasipotential approximation error depends on the perturbation size.

The reduction simplifies multidimensional escape problems to one-dimensional analysis.

Applicable to systems close to reversibility with stable stationary curves.

Abstract

We consider n-dimensional deterministic flows obtained by perturbing a gradient flow. We assume that the gradient flow admits a stable curve of stationary points, and thus if the perturbation is not too large the perturbed flow also admits an attracting curve. We show that the noise induced escape problem from a stable fixed point of this curve can be reduced to a one-dimensional problem: we can approximate the associated quasipotential by the one associated to the restricted dynamics on the stable curve. The error of this approximation is given in terms of the size of the perturbation.