Stochastic resonance and noise delayed extinction in a model of two competing species

TL;DR

This paper investigates how stochastic noise influences the dynamics and extinction times of two competing species, revealing noise-induced oscillations, stochastic resonance, and nonmonotonic extinction behavior in a stochastic Lotka-Volterra model.

Contribution

It introduces a stochastic Lotka-Volterra model with a bistable interaction parameter driven by noise and periodic forcing, highlighting new noise-induced phenomena in species competition.

Findings

Noise induces periodic oscillations in species concentrations.

Stochastic resonance enhances species coexistence under certain noise levels.

Extinction time exhibits nonmonotonic dependence on noise intensity.

Abstract

We study the role of the noise in the dynamics of two competing species. We consider generalized Lotka-Volterra equations in the presence of a multiplicative noise, which models the interaction between the species and the environment. The interaction parameter between the species is a random process which obeys a stochastic differential equation with a generalized bistable potential in the presence of a periodic driving term, which accounts for the environment temperature variation. We find noise-induced periodic oscillations of the species concentrations and stochastic resonance phenomenon. We find also a nonmonotonic behavior of the mean extinction time of one of the two competing species as a function of the additive noise intensity.