1. A. Duvall, M. Ali Al-Radhawi, Dhruv D. Jatkar, and E. D. Sontag. Interplay between contractivity and monotonicity for reaction networks. SIAM J Applied Dynamical Systems, 2024. Note: Submitted. Also preprint in https://arxiv.org/abs/2404.18734 .[PDF] Keyword(s): reaction networks, monotone systems, reaction networks, reaction networks, contractive systems. Abstract:

   This work studies relationships between monotonicity and contractivity, and applies the results to establish that many reaction networks are weakly contractive, and thus, under appropriate compactness conditions, globally convergent to equilibria. Verification of these properties is achieved through a novel algorithm that can be used to generate cones for an accompanying monotone system. The results given here allow a unified proof of global convergence for several classes of networks that had been previously studied in the literature.

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