论文标题
伪装的复要动力系统
Disguised toric dynamical systems
论文作者
论文摘要
我们研究了受生化反应网络启发的多项式动力学系统的家族。我们专注于复杂的平衡质量成分系统，这些系统也称为复合物。它们已知或猜想是具有非常强大的动力学特性，例如积极稳态，局部和全球稳定性，持久性和永久性的存在和独特性。我们考虑包含感谢您的动力学系统的伪装的复曲面动力系统，上面提到的所有动力学属性自然扩展到其中。通过（真实）代数几何形状，我们表明某些反应网络具有空的紫红色基因座或lebesgue的曲折基因座，在参数空间中测量零，而它们的伪装的曲折locus则具有正度度量。我们还提出了一些可以用来检测伪装的曲折基因座的算法。
We study families of polynomial dynamical systems inspired by biochemical reaction networks. We focus on complex balanced mass-action systems, which have also been called toric. 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 of disguised 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 an empty toric locus or a toric locus of Lebesgue measure zero in parameter space, while their disguised toric locus is of positive measure. We also propose some algorithms one can use to detect the disguised toric locus.
