Algorithmic Global Criteria for Excluding Oscillations
Algorithmic Global Criteria for Excluding Oscillations
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DOI：
10.1007/s11538-010-9618-0
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发表时间：
2011-01
影响因子：
3.5
通讯作者：
A. Weber;T. Sturm;E. O. Abdel-Rahman
中科院分区：
文献类型：
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作者：
A. Weber;T. Sturm;E. O. Abdel-Rahman
我们研究算法的方法来解决以下问题：给定一个系统的参数常微分方程建立的生物模型，是否存在的范围内的值的模型参数和变量都是有意义的，从生物学的角度来看，振荡的轨迹，可以找到？我们表明，在常见的情况下，多项式向量场已知的标准，排除存在的非常数极限环导致量词消除问题的reals.We应用这些标准，以前已经调查的背景下，代数生物学的各种模型。
We investigate algorithmic methods to tackle the following problem: Given a system of parametric ordinary differential equations built by a biological model, does there exist ranges of values for the model parameters and variables which are both meaningful from a biological point of view and where oscillating trajectories, can be found? We show that in the common case of polynomial vector fields known criteria excluding the existence of non-constant limit cycles lead to quantifier elimination problems over the reals.We apply these criteria to various models that have been previously investigated in the context of algebraic biology.