Chemical Kinetics

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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.