Computationally Checking if a Reaction Network is Monotone or Non-expansive

TL;DR

This paper introduces a systematic method to determine whether reaction networks are monotone or non-expansive by identifying suitable norms and cones, and proves duality relationships, enhancing understanding of network dynamics.

Contribution

It provides a novel, systematic procedure for testing monotonicity and non-expansivity in reaction networks, including proofs of impossibility and duality relationships.

Findings

Reproduces known results in reaction network analysis.

Identifies conditions under which networks are non-expansive or monotone.

Shows certain networks cannot be monotone or non-expansive under any norm or cone.

Abstract

We present a systematic procedure for testing whether reaction networks exhibit non-expansivity or monotonicity. This procedure identifies explicit norms under which a network is non-expansive or cones for which the system is monotone-or provides proof that no such structures exist. Our approach reproduces known results, generates novel findings, and demonstrates that certain reaction networks cannot exhibit monotonicity or non-expansivity with respect to any cone or norm. Additionally, we establish a duality relationship which states that if a network is monotone, so is its dual network.