Convergence to equilibrium in competitive Lotka-Volterra equations

TL;DR

This paper proves that a generalized system of competitive Lotka-Volterra equations converges to a unique stable equilibrium, using adapted techniques from previous studies on biological population models.

Contribution

It introduces a novel approach to demonstrate convergence to equilibrium in generalized competitive Lotka-Volterra systems.

Findings

Proves convergence to a unique stable equilibrium.

Extends techniques to more generalized models.

Provides theoretical guarantees for stability.

Abstract

We study a generalized system of ODE's modeling a finite number of biological populations in a competitive interaction. We adapt the techniques in two previous articles to prove the convergence to a unique stable equilibrium.