SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 3, Page 1798-1822, January 2020.
An important dynamical property of biological interaction networks is persistence, which intuitively means that “no species goes extinct." It has been conjectured that dynamical system models of weakly reversible networks (i.e., networks for which each reaction is part of a cycle) are persistent. The property of persistence is also related to the well-known global attractor conjecture. An approach for the proof of the global attractor conjecture uses an embedding of weakly reversible dynamical systems into toric differential inclusions. We show that the larger class of endotactic dynamical systems can also be embedded into toric differential inclusions. Moreover, we show that, essentially, endotactic networks form the largest class of networks with this property.

中文翻译：

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内分泌网络和复曲面微分包含

SIAM应用动力系统杂志，第19卷第3期，第1798-1822页，2020年1月。
持久性是生物相互作用网络的一个重要的动力学特性，它的直观含义是“没有物种灭绝。”据推测，弱可逆网络（即每个反应是循环的一部分的网络）的动力学系统模型是持久的。持久性的性质还与著名的全局吸引子猜想有关。一种证明全局吸引子猜想的方法是将弱可逆动力学系统嵌入复曲面微分包含物中。我们证明了更大范围的内趋动力学系统还可以将其嵌入到复曲面微分包含物中，而且，从本质上讲，我们表明内分泌网络构成了具有此特性的最大类网络。