Noise delayed decay of unstable states: theory versus numerical simulations

TL;DR

This paper investigates how noise influences the decay times of unstable states in nonlinear systems, providing exact formulas and demonstrating nonmonotonic behavior through analytical and numerical comparisons.

Contribution

It offers exact decay time expressions for polynomial potentials and reveals nonmonotonic noise effects, bridging theory and numerical simulations.

Findings

Decay times exhibit nonmonotonic dependence on noise intensity.

Analytical formulas match numerical simulation results.

Noise can both delay and accelerate decay of unstable states.

Abstract

We study the noise delayed decay of unstable nonequilibrium states in nonlinear dynamical systems within the framework of the overdamped Brownian motion model. We give the exact expressions for the decay times of unstable states for polynomial potential profiles and obtain nonmonotonic behavior of the decay times as a function of the noise intensity for the unstable nonequilibrium states. The analytical results are compared with numerical simulations.