Systems of interacting species, such as biological environments or chemical reactions, are often described mathematically by sets of coupled ordinary differential equations. While a large number β of species may be involved in the coupled dynamics, often only α<β species are of interest or of consequence. In this paper, we explored how to construct models that include only those given α species, but still recreate the dynamics of the original β-species model. Under some conditions detailed here, this reduction can be completed exactly, such that the information in the reduced model is exactly the same as the original one, but over fewer equations. Moreover, this reduction process suggests a promising type of approximate model—no longer exact, but computationally quite simple.
Parameter Identification For Oscillating Chemical Reactions Modelled By Systems Of Ordinary Differential Equations
