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

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.