Chemical Kinetics

研究的对象是化学反应网络。一组反应产生了混合良好的常微分方程组 情形和空间非均匀情形下的一组反应扩散方程。主要应用领域是生化反应网络，它 通常在系统生物学中使用。有两个主要目标：(1)确定这些系统何时具有规则的动力学：每个解往往 平衡(在反应-扩散系统中为齐次平衡)；(2)确定何时有可能减少到较小的系统 这捕捉到了原始系统的动态。在(1)下，我们试图完成全局吸引子猜想的证明，研究具有以下性质的系统 不同类型的动力学，并考虑具有不同扩散常数的反应扩散系统。减少化学物质的新方法 本课程将探讨隔室系统的反应网络。在(2)项下，我们试图确定何时有两种新的系统方法来减少系统 提供良好的近似，并探索更高维度的全局定义的慢流形。这项研究是对其他调查的补充 更复杂的动力学，如多稳性、振荡和图案形成。这将对生物建模产生影响 因为我们试图理解大规模的生化反应网络。

The subject of study is chemical reaction networks. A set of reactions gives rise to a system of ordinary differential equations in the well--mixed case and a set of reaction-diffusion equations in the spatially inhomogeneous case. The main area of applications is biochemical reaction networks which are commonly used in systems biology. There are two major goals: (1) to determine when these systems have regular dynamics: every solution tends to an 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 with different kinds of kinetics and consider reaction-diffusion systems with different diffusion constants. The new approach of reducing a chemical reaction network to a compartmental system will be explored. Under (2), we seek to determine when two new systematic ways of reducing a system provide good approximations and explore globally defined slow manifolds in higher dimensions. This research is complementary to other investigations of more complicated dynamics such as multistability, oscillations and pattern formation. There will be implications for biological modeling as we attempt to understand large-scale biochemical reaction networks.