Extinction behaviour for mutually enhancing continuous-state population dynamics

TL;DR

This paper investigates the extinction behavior of a two-species continuous-state population model described by a coupled stochastic differential equation system with mutual enhancement, driven by Brownian motion and stable noise.

Contribution

It introduces a novel two-dimensional SDE model with mutual enhancement and analyzes its extinction properties under various coefficient conditions.

Findings

Extinction probabilities depend on the coefficients of the SDEs.

The model exhibits different extinction regimes based on parameter choices.

The system generalizes classical Lotka-Volterra models with stochastic influences.

Abstract

In this paper, we study a two-dimensional process arising as the unique nonnegative solution to a system of two stochastic differential equations (SDEs) with mutually enhancing two-way interactions driven by independent Brownian motions and spectrally positive $\alpha$-stable random measures. Such a SDE system can be identified as a continuous-state Lotka-Volterra type population model. Extinction properties of the populations are studied for different choices of the coefficients involved in the SDEs.