Coexistence and Exclusion of Stochastic Competitive Lotka-Volterra Models
Dang Hai Nguyen, George Yin
TL;DR
This paper establishes conditions for coexistence and exclusion in stochastic competitive Lotka-Volterra models, along with convergence results and numerical illustrations, advancing understanding of stochastic ecological dynamics.
Contribution
It provides near-necessary conditions for coexistence and exclusion, and proves convergence in distribution of solutions, which are novel theoretical insights.
Findings
Conditions for coexistence and exclusion derived
Convergence in distribution of solutions proved
Numerical examples illustrate theoretical results
Abstract
This work derives sufficient conditions for the coexistence and exclusion of a stochastic competitive Lotka-Volterra model. The conditions obtained are close to the necessary conditions. In addition, convergence in distribution of positive solutions of the model is also established. A number of numerical examples are given to illustrate our results.
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