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.