  Under suitable assumptions, the dynamic behaviour of a chemical reaction
network is governed by an autonomous set of polynomial ordinary differential
equations over continuous variables representing the concentrations of the
reactant species. It is known that two networks may possess the same governing
mass-action dynamics despite disparate network structure. To date, however,
there has only been limited work exploiting this phenomenon even for the cases
where one network possesses known dynamics while the other does not. In this
paper, we bring these known results into a broader unified theory which we call
conjugate chemical reaction network theory. We present a theorem which gives
conditions under which two networks with different governing mass-action
dynamics may exhibit the same qualitative dynamics and use it to extend the
scope of the well-known theory of weakly reversible systems.
