New noise-induced statistically steady state in the spatially extended competition model

TL;DR

This paper explores how external noise influences species competition in a spatial model, revealing a new steady state where the weaker species outcompetes the stronger one due to stochastic effects.

Contribution

It introduces a novel noise-induced steady state in a spatial competition model where the weaker species displaces the stronger one.

Findings

Existence of a new noise-induced steady state with species displacement.

Confirmation that noise can alter competitive dominance in spatial systems.

Demonstration through numerical analysis that stochastic effects lead to coexistence or displacement.

Abstract

The influence of an external random field on the competition process in a nonlinear open spatially extended system is analyzed numerically. A three-component model is chosen as the competition model in which a "weak" species can move in space and the rate of the resource density growth fluctuates in space and in time [A.S. Mikhailov and I.V. Uporov, Usp. Sov. Phys. Usp. 27, 695 (1984)]. It is demonstrated that in addition to the noise-induced statistically steady state found by the authors [Sov. Phys. Usp. 27, 695 (1984)], in which both species can coexist, there exists another noise-induced statistically steady state, in which the "weak" species displaces the "strong" species, i.e. the "strong" species at an average asymptotically disappears.