Chemical Kinetics

研究的主题是化学反应网络。一组反应产生一个常微分方程组， 的情况下和一组反应扩散方程的空间非齐次的情况下。 主要应用领域是生化反应网络， 通常用于系统生物学。 有两个主要目标：（1）确定这些系统何时具有规则动力学：每个解都倾向于 平衡（反应扩散系统中的齐次平衡）;（2）确定何时可以简化为更小的系统 捕捉原始系统的动态。 在（1）中，我们试图完成全局吸引子猜想的证明，研究具有 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 反应网络的一个房室系统将被探讨。 在（2）中，我们试图确定何时两种新的系统化方法还原一个系统 提供良好的近似和探索全球定义的慢流形在更高的维度。 这项研究是对其他调查的补充 更复杂的动力学，如多稳定性，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.