Chemical Kinetics

研究的主题是化学反应网络。在充分混合的情况下，一组反应产生一组常微分方程，在空间非齐次的情况下，一组反应-扩散方程。应用的主要领域是系统生物学中常用的生化反应网络。有两个主要目标：(1)确定这些系统何时具有规则动力学：每个溶液趋于平衡（在反应扩散系统的情况下为均匀平衡）；(2)确定何时可以将其缩减为一个更小的系统，以捕获原始系统的动态。在(1)项下，我们寻求完成全局吸引子猜想的证明，研究具有不同动力学类型的系统，并考虑具有不同扩散常数的反应-扩散系统。将探索将化学反应网络还原为隔室系统的新方法。在(2)中，我们试图确定两种新的系统化简方法何时提供良好的近似，并探索全局定义的高维慢流形。这项研究是对其他更复杂的动力学研究的补充，如多稳定性、振荡和模式形成。当我们试图理解大规模的生化反应网络时，这将对生物建模产生影响。

The subject of study is chemical reaction networks. A set of reactions gives rise to a system of ordinary differential equations in the well--mixedcase and a set of reaction-diffusion equations in the spatially inhomogeneous case. The main area of applications is biochemical reaction networks whichare commonly used in systems biology. There are two major goals: (1) to determine when these systems have regular dynamics: every solution tends toan equilibrium (homogeneous equilibrium in the case of reaction-diffusion systems); (2) to determine when it is possible to reduce to a smaller system that captures the dynamics of the original system. Under (1), we seek to finish the proof of the global attractor conjecture, study systems withdifferent kinds of kinetics and consider reaction-diffusion systems with different diffusion constants. The new approach of reducing a chemicalreaction network to a compartmental system will be explored. Under (2), we seek to determine when two new systematic ways of reducing a systemprovide good approximations and explore globally defined slow manifolds in higher dimensions. This research is complementary to other investigationsof more complicated dynamics such as multistability, oscillations and pattern formation. There will be implications for biological modelingas we attempt to understand large-scale biochemical reaction networks.