Chemical Kinetics

研究的对象是化学反应网络。在混合良好的情况下，一组反应产生一组常微分方程组，在空间不均匀的情况下，产生一组反应扩散方程。主要的应用领域是生化反应网络，这是系统生物学中常用的。有两个主要目标：(1)确定这些系统何时具有规则的动力学：每个解趋于*平衡(在反应-扩散系统的情况下为齐次平衡)；(2)确定何时可能简化为一个较小的系统*，以捕捉原始系统的动态。在(1)下，我们试图完成整体吸引子猜想的证明，研究具有不同类型动力学的系统，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简化为隔室系统的新方法。在(2)中，我们试图确定何时有两种新的系统化简方法*提供良好的逼近，并探索高维的全局定义的慢流形。这项研究是对更复杂动力学的其他研究的补充，如多稳定性、振荡和图案形成。随着我们试图理解大规模的生化反应网络，这将对生物学建模产生影响。

The subject of study is chemical reaction networks. A set of reactions gives rise to a system of ordinary differential equations in the well--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.