Disguised toric dynamical systems
Disguised toric dynamical systems
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DOI：
10.1016/j.jpaa.2022.107035
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发表时间：
2020-06
影响因子：
0.8
通讯作者：
Laura Brustenga i Moncus'i;G. Craciun;Miruna-Stefana Sorea
中科院分区：
文献类型：
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作者：
Laura Brustenga i Moncus'i;G. Craciun;Miruna-Stefana Sorea
受生化反应网络的启发，我们研究了一族多项式动力系统。我们将重点放在复杂的平衡质量作用系统上，这也被称为动力学。已知或猜测它们具有非常强的动力学性质，如正定态的存在唯一性、局部和全局稳定性、持久性和持久性。我们考虑了一类伪环面动力系统，它包含了环面动力系统，并且上述所有的动力学性质都是自然推广的。借助于(实)代数几何的方法，我们证明了某些反应网络在参数空间中有勒贝格测度零的空迹或环迹，而它们的伪迹是正测度。我们还提出了可用于检测伪装圆环轨迹的算法。
We study families of polynomial dynamical systems inspired by biochemical reaction networks. We focus oncomplex balanced mass-action systems, which have also been calledtoric. They are known or conjectured to enjoy very strong dynamical properties, such as existence and uniqueness of positive steady states, local and global stability, persistence, and permanence. We consider the class ofdisguised toric dynamical systems, which contains toric dynamical systems, and to which all dynamical properties mentioned above extend naturally. By means of (real) algebraic geometry we show that some reaction networks have anemptytoric locus or a toric locus of Lebesgue measure zero in parameter space, while theirdisguisedtoric locus is of positive measure. We also proposesome algorithmsone can use to detect the disguised toric locus.