通过弱可逆网络与全局吸引轨迹的实现
Realizations through Weakly Reversible Networks and the Globally Attracting Locus
AI总结：
本文研究用弱可逆网络再现给定质量作用动力学的条件，证明二维强内趋网络及部分附加条件下的内趋网络具有该性质，并将其与全局稳定稳态轨迹联系起来。
摘要：
我们研究了如下可能性：对于与网络 G 相关联的任意给定反应速率向量 k，是否存在另一个网络 G′，其相应的反应速率向量能够再现由 (G,k) 生成的质量作用动力学。我们关注 G 的一类特定网络，其中相应的网络 G′ 是弱可逆的。特别地，我们证明了具有二维化学计量子空间的强内趋二维网络，以及在附加条件下的某些内趋网络，都展现出这一性质。此外，我们在这一网络族与速率常数空间中的轨迹之间建立了紧密联系，对该轨迹而言，相应动力学具有全局稳定稳态。
英文摘要：
We investigate the possibility that for any given reaction rate vector $k$ associated with a network $G$, there exists another network $G'$ with a corresponding reaction rate vector that reproduces the mass-action dynamics generated by $(G,k)$. Our focus is on a particular class of networks for $G$, where the corresponding network $G'$ is weakly reversible. In particular, we show that strongly endotactic two-dimensional networks with a two dimensional stoichiometric subspace, as well as certain endotactic networks under additional conditions, exhibit this property. Additionally, we establish a strong connection between this family of networks and the locus in the space of rate constants of which the corresponding dynamics admits globally stable steady states.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
