Weakly reversible and deficiency zero reaction networks form the main cast of the Deficiency Zero Theorem. At the same time, it has been recognized that to have the dynamics of a complex-balanced system, $(G,k)$ may not itself be complex-balanced, but is instead dynamically equivalent to a complex-balanced system $(G*,k*)$. In general, there may be multiple complex-balanced realizations for a given ODE. We proved that there can be at most one weakly reversible and deficiency zero realization, and uniqueness no longer holds when either assumption is dropped. From our result, we also obtained a simple algorithm for whether such a realization exists. 

This is joint work with Gheorghe Craciun and Jiaxin Jin.

Google Meet link: https://meet.google.com/bgt-oqys-gme