A coordinate-independent theory for multi-time-scale dynamical systems

生化反应网络在许多不同的时间尺度上固有地运行，识别这种时间层次是理解生物行为的关键。目前，现有的动力系统理论不能严格地分析许多重要的生物系统和网络，由于这种固有的非标准的多时间尺度分裂。该项目旨在消除这些障碍，并开发一种独立于坐标的数学理论，将几何奇异摄动理论、微分和代数几何以及反应网络理论的结果编织在一起，以分解和解释非标准多时间尺度系统和网络中事件的动态层次结构。

Biochemical reaction networks operate inherently on many disparate timescales, and identifying this temporal hierarchy is key to understanding biological behaviour. Currently, the existing dynamical systems theory is not able to rigorously analyse many important biological systems and networks due to this inherent non-standard multi-time-scale splitting. This project aims to remove these stumbling blocks and develop a coordinate-independent mathematical theory that weaves together results from geometric singular perturbation theory, differential and algebraic geometry and reaction network theory to decompose and explain the structure in the dynamic hierarchy of events in non-standard multi-time-scale systems and networks.