Extinction behaviour for competing continuous-state population dynamics

TL;DR

This paper analyzes a stochastic Lotka-Volterra model with Brownian and stable noise, establishing nearly sharp conditions under which one population goes extinct, advancing understanding of stochastic population dynamics.

Contribution

It introduces nearly sharp extinction criteria for a two-species stochastic differential equation system with complex noise sources.

Findings

Derived conditions for population extinction

Identified impact of stable and Brownian noise on dynamics

Enhanced understanding of stochastic competition models

Abstract

We consider a system of two stochastic differential equations (SDEs) with competing two-way interactions driven by Brownian motions and spectrally positive $\alpha$-stable random measures. Such a SDE system can be identified as a Lotka-Volterra type population model. We find nearly sharp conditions for one of the population to become extinct or extinguished.