A projection argument for differential inclusions, with applications to persistence of mass-action kinetics
A projection argument for differential inclusions, with applications to persistence of mass-action kinetics
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微分夹杂物的投影论证，及其在质量作用动力学持久性中的应用
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Anne Shiu
中科院分区：
文献类型：
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作者：
Manoj Gopalkrishnan;Ezra Miller;Anne Shiu
受质量作用动力学问题的启发，我们引入了微分夹杂物的顶点族的概念。这些族在开放超立方体上定义，其特点是在投影图下具有特别良好的行为。激励性的例子是某些反应网络家族{包括可逆、弱可逆、内规和强内规反应网络{，它们产生质量作用微分包含物的垂直家族。我们证明顶点族适合结构归纳。因此，当且仅当顶点族的轨迹接近超立方体的顶点，或者族的低维成员中的轨迹接近边界时，顶点族的轨迹才接近边界。借助这项技术，我们在全局吸引子猜想上取得了进展，这是一个有关质量作用动力学系统的核心开放问题。此外，我们将质量作用动力学称为具有可变速率的反应网络上的函子。
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.
化学反应网络产生的微分方程组的全局收敛
DOI：
10.48550/arxiv.1205.1716
发表时间：
2012
期刊：
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影响因子：
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作者：
Banaji M
通讯作者：
Banaji M