[数学] 三重动力系统 [推广有奖]

摘要翻译：
在数学化学文献中，多曲动力系统被称为复杂平衡质量作用系统，它们的许多显着性质已经被证实。它们包括作为特例的所有不足零系统和所有详细的平衡系统。一个特点是，一个多曲面动力系统的稳态轨迹是一个多曲面变体，它在每个不变多面体内都有一个唯一的点。在计算代数几何的背景下，我们发展了多环动力系统的基本理论，并证明了相关模空间也是一个多环变体。推测复平衡态是全局吸引子。对于不变多面体是二维有界的详细平衡系统，我们证明了这一点。
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英文标题：
《Toric dynamical systems》
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作者：
Gheorghe Craciun, Alicia Dickenstein, Anne Shiu, Bernd Sturmfels
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最新提交年份：
2007
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分类信息：

一级分类：Mathematics        数学
二级分类：Dynamical Systems        动力系统
分类描述：Dynamics of differential equations and flows, mechanics, classical few-body problems, iterations, complex dynamics, delayed differential equations
微分方程和流动的动力学，力学，经典的少体问题，迭代，复杂动力学，延迟微分方程
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一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
  Toric dynamical systems are known as complex balancing mass action systems in the mathematical chemistry literature, where many of their remarkable properties have been established. They include as special cases all deficiency zero systems and all detailed balancing systems. One feature is that the steady state locus of a toric dynamical system is a toric variety, which has a unique point within each invariant polyhedron. We develop the basic theory of toric dynamical systems in the context of computational algebraic geometry and show that the associated moduli space is also a toric variety. It is conjectured that the complex balancing state is a global attractor. We prove this for detailed balancing systems whose invariant polyhedron is two-dimensional and bounded.
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PDF链接：
https://arxiv.org/pdf/0708.3431