Time dependence of moments of an exactly solvable Verhulst model under random perturbations

TL;DR

This paper derives explicit formulas for the moments of a stochastic Verhulst model influenced by Markovian coloured noise, showing their exponential decay and asymptotic behavior over time.

Contribution

It provides exact expressions for moments of the stochastic Verhulst model under coloured noise, highlighting their time dependence and asymptotic properties.

Findings

Moments decay exponentially over time.

Asymptotic behavior characterized by a single exponent.

Explicit formulas for moments under Markovian coloured noise.

Abstract

Explicit expressions for one point moments corresponding to stochastic Verhulst model driven by Markovian coloured dichotomous noise are presented. It is shown that the moments are the given functions of a decreasing exponent. The asymptotic behavior (for large time) of the moments is described by a single decreasing exponent.