Noise-intensity fluctuation in Langevin model and its higher-order Fokker-Planck equation

TL;DR

This paper explores how stochastic fluctuations in noise intensity affect Langevin systems, deriving a higher-order Fokker-Planck equation and revealing bimodal-to-trimodal transitions in probability distributions across various models.

Contribution

It introduces a higher-order Fokker-Planck equation accounting for noise-intensity fluctuations and demonstrates their impact on system distributions, validated by simulations.

Findings

Noise fluctuations induce bimodal-to-trimodal transitions.

Higher-order Fokker-Planck equation effectively models noise effects.

Distributions validated with Monte Carlo simulations.

Abstract

In this paper, we investigate a Langevin model subjected to stochastic intensity noise (SIN), which incorporates temporal fluctuations in noise-intensity. We derive a higher-order Fokker-Planck equation (HFPE) of the system, taking into account the effect of SIN by the adiabatic elimination technique. Stationary distributions of the HFPE are calculated by using the perturbation expansion. We investigate the effect of SIN in three cases: (a) parabolic and quartic bistable potentials with additive noise, (b) a quartic potential with multiplicative noise, and (c) a stochastic gene expression model. We find that the existence of noise intensity fluctuations induces an intriguing phenomenon of a bimodal-to-trimodal transition in probability distributions. These results are validated with Monte Carlo simulations.