A simple proof of monotonicity for linear cooperative systems of ODEs

TL;DR

This paper offers a straightforward proof demonstrating the monotonicity property of linear cooperative systems of ODEs, simplifying previous approaches that relied on approximation methods.

Contribution

It introduces a simple, direct proof of monotonicity for linear cooperative ODE systems, avoiding the need for approximation by strongly cooperative systems.

Findings

Proof simplifies understanding of monotonicity in cooperative systems

Eliminates the need for approximation techniques in proofs

Enhances theoretical foundations of cooperative ODE analysis

Abstract

We present a simple proof of monotonicity for cooperative systems of linear ordinary differential equations, without having recourse to approximation by strongly cooperative systems.