  The induced kinetic differential equation of a reaction network endowed with
mass action type kinetics is a system of polynomial differential equations. The
problem studied here is: Given a polynomial differential equation, is it
possible to find a network which induces the equation? If yes, can we find a
network with some chemically relevant properties (implying also important
dynamic consequences), such as reversibility, weak reversibility, zero
deficiency, detailed balancing, complex balancing, mass conservation, etc. The
constructive answers presented to a series of questions of the above type are
useful when fitting a differential equation to measurements, or when trying to
find out the dynamic behavior of the solutions of a differential equation. It
turns out that some of the results can be applied when trying to solve purely
mathematical problems, like the existence of positive solutions to polynomial
equation.
