On the dynamics of interacting populations in presence of state dependent fluctuations

TL;DR

This paper explores stochastic models of interacting populations with state-dependent parameters influenced by environmental noise, leading to nonlinear differential equations and, in some cases, Fokker-Planck equations for population densities.

Contribution

It introduces a framework for modeling population dynamics with stochastic, state-dependent parameters and derives corresponding probability density equations.

Findings

Models incorporate environmental noise into population interactions.

Reduction to Fokker-Planck equations in specific cases.

Highlights the impact of stochastic fluctuations on population stability.

Abstract

We discuss several models of the dynamics of interacting populations. The models are constructed by nonlinear differential equations and have two sets of parameters: growth rates and coefficients of interaction between populations. We assume that the parameters depend on the densities of the populations. In addition the parameters can be influenced by different factors of the environment. This influence is modelled by noise terms in the equations for the growth rates and interaction coefficients. Thus the model differential equations become stochastic. In some particular cases these equations can be reduced to a Foker-Plancnk equation for the probability density function of the densities of the interacting populations.