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摘要翻译：
生物学家和数学家都对显示双稳态的生化模型感兴趣。化学反应网络理论一方面可以提供双稳态存在的充分条件，另一方面可以排除多稳态存在的可能性。了解小网络是重要的，因为生化模型的子网络中存在多个稳态，有时可以在大网络中建立多平稳性。本文建立了允许双稳态的最小可逆保质量网络，并确定了存在多个稳态的参数的半代数集。
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英文标题：
《The smallest multistationary mass-preserving chemical reaction network》
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作者：
Anne Shiu
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最新提交年份：
2008
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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：
Biochemical models that exhibit bistability are of interest to biologists and mathematicians alike. Chemical reaction network theory can provide sufficient conditions for the existence of bistability, and on the other hand can rule out the possibility of multiple steady states. Understanding small networks is important because the existence of multiple steady states in a subnetwork of a biochemical model can sometimes be lifted to establish multistationarity in the larger network. This paper establishes the smallest reversible, mass-preserving network that admits bistability and determines the semi-algebraic set of parameters for which more than one steady state exists.
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PDF链接：
https://arxiv.org/pdf/0801.3689
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