Realizations of kinetic differential equations
Realizations of kinetic differential equations
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DOI：
10.3934/mbe.2020046
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发表时间：
2020-01-01
影响因子：
2.6
通讯作者：
Yu, Polly Y.
中科院分区：
文献类型：
--
作者：
Craciun, Gheorghe;Johnston, Matthew D.;Yu, Polly Y.
具有质量作用型动力学的反应网络的诱导动力学微分方程是一个多项式微分方程组。这里研究的问题是：给定一个多项式微分方程组，是否有可能找到一个网络来导出这些方程;换句话说：是否有可能找到这个微分方程组的动力学实现？如果是，我们能否找到一个具有某些化学相关性质（也意味着重要的动力学后果）的网络，如可逆性、弱可逆性、零亏、详细平衡、复杂平衡、质量守恒等？当将微分方程拟合到数据集时，或者当试图找出微分方程解的动态行为时，对上述类型的一系列问题提出的建设性答案是有用的。事实证明，其中一些结果可以应用于解决看似无关的数学问题，如代数方程正解的存在性。
The induced kinetic differential equations of a reaction network endowed with mass action type kinetics is a system of polynomial differential equations. The problem studied here is: Given a system of polynomial differential equations, is it possible to find a network which induces these equations; in other words: is it possible to find a kinetic realization of this system of differential equations? If yes, can we find a network with some chemically relevant properties (implying also important dynamic consequences), such as reversibility, weak reversibility, zero deficiency, detailed balancing, complex balancing, mass conservation, etc.? The constructive answers presented to a series of questions of the above type are useful when fitting differential equations to datasets, or when trying to find out the dynamic behavior of the solutions of differential equations. It turns out that some of these results can be applied when trying to solve seemingly unrelated mathematical problems, like the existence of positive solutions to algebraic equations.