LMI approach to global stability analysis of stochastic delayed Lotka-Volterra models

TL;DR

This paper develops a Linear Matrix Inequality (LMI) based method to analyze the global stability of stochastic delayed Lotka-Volterra models, providing practical conditions and numerical validation for ecological systems with delays and randomness.

Contribution

It introduces a novel LMI-based approach for stability analysis of stochastic delayed Lotka-Volterra systems, extending existing methods to include both discrete and distributed delays with stochastic perturbations.

Findings

Derived sufficient LMI conditions for stability

Validated method with numerical examples

Applicable to systems with discrete and distributed delays

Abstract

This paper is devoted to the stability analysis of an n species Lotka-Volterra system with discrete and distributed delays. Stochastic perturbations to the parameters of the model are allowed. Sufficient conditions for the almost sure global asymptotic stability of the positive equilibrium are derived in terms of LMIs. The efficiency of the proposed method is illustrated by numerical examples.