伪装复曲面动力系统
Disguised toric dynamical systems
摘要：
我们研究受生化反应网络启发的多项式动力系统族。我们专注于复杂的平衡质量作用系统，也被称为复曲面。它们具有很强的动力学性质，如正平衡态的存在性和唯一性、局部和全局稳定性、持久性和持久性。我们考虑一类伪装复曲面动力系统，它包含复曲面动力系统，并且上面提到的所有动力学性质自然地延伸到它。利用（实）代数几何方法证明了某些反应网络在参数空间中存在空复曲面轨迹或勒贝格测度为零的复曲面轨迹，而它们的伪装复曲面轨迹是正测度的.我们还提出了一些算法，可以用来检测伪装复曲面轨迹。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
