微分包含的投影论证及其在质量作用动力学持久性中的应用
A Projection Argument for Differential Inclusions, with Applications to Persistence of Mass-Action Kinetics
AI总结：
引入顶点族微分包含概念，通过投影映射的良好性质，利用结构归纳法证明轨迹趋近边界等价于趋近超立方体顶点或低维成员轨迹趋近边界，推进了质量作用动力学系统的全局吸引子猜想。
摘要：
受质量作用动力学问题的启发，我们引入了微分包含的顶点族概念。这些族定义在开超立方体上，其特点是在投影映射下具有特定的良好行为。激励例子是某些反应网络族——包括可逆、弱可逆、内切和强内切反应网络——它们产生质量作用微分包含的顶点族。我们证明了顶点族适用于结构归纳法。因此，顶点族的轨迹趋近边界当且仅当要么轨迹趋近超立方体的顶点，要么族中低维成员的轨迹趋近边界。利用这一技术，我们在全局吸引子猜想（关于质量作用动力学系统的一个核心开放问题）上取得了进展。此外，我们将质量作用动力学表述为关于具有可变速率的反应网络的函子。
英文摘要：
Motivated by questions in mass-action kinetics, we introduce the notion of vertexical family of differential inclusions. Defined on open hypercubes, these families are characterized by particular good behavior under projection maps. The motivating examples are certain families of reaction networks -- including reversible, weakly reversible, endotactic, and strongly endotactic reaction networks -- that give rise to vertexical families of mass-action differential inclusions. We prove that vertexical families are amenable to structural induction. Consequently, a trajectory of a vertexical family approaches the boundary if and only if either the trajectory approaches a vertex of the hypercube, or a trajectory in a lower-dimensional member of the family approaches the boundary. With this technology, we make progress on the global attractor conjecture, a central open problem concerning mass-action kinetics systems. Additionally, we phrase mass-action kinetics as a functor on reaction networks with variable rates.
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。
