Interplay between Contractivity and Monotonicity for Reaction Networks

Alon Duvall, M. Ali Al-Radhawi, Dhruv D. Jatkar, Eduardo Sontag
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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 monotone systems. 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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反应网络的契约性与单调性之间的相互作用
这项工作研究了单调性和收缩性之间的关系,并应用研究结果确定了许多反应网络具有弱收缩性,因此,在适当的紧凑性条件下,可以全局收敛到平衡状态。这些性质的验证是通过一种新颖的算法实现的,该算法可用于生成单调系统的锥体。本文给出的结果可以统一证明以前文献中研究过的几类网络的全局收敛性。
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