Stationary distributions of a noisy logistic process

TL;DR

This paper derives stationary distributions for a noisy logistic process, revealing how correlated noise can induce stochastic resonance and minimize variance, even in systems with unbounded growth.

Contribution

It constructs stationary solutions for a Fokker-Planck equation with correlated Gaussian noises in a logistic model, highlighting novel effects of noise correlation.

Findings

Stationary distributions exist despite unbounded deterministic growth.

Positive noise correlation can minimize process variance.

Correlated noise can induce stochastic resonance with periodic driving.

Abstract

Stationary solutions to a Fokker-Planck equation corresponding to a noisy logistic equation with correlated Gaussian white noises are constructed. Stationary distributions exist even if the corresponding deterministic system displays an unlimited growth. Positive correlations between the noises can lead to a minimum of the variance of the process and to the stochastic resonance if the system is additionally driven by a periodic signal.