  Systems of differential equations with polynomial right-hand sides are very
common in applications. On the other hand, their mathematical analysis is very
challenging in general, due to the possibility of complex dynamics: multiple
basins of attraction, oscillations, and even chaotic dynamics. Even if we
restrict our attention to mass-action systems, all of these complex dynamical
behaviours are still possible. On the other hand, if a polynomial dynamical
system has a weakly reversible deficiency zero ($WR_0$) realization, then its
dynamics is known to be remarkably simple: oscillations and chaotic dynamics
are ruled out and, up to linear conservation laws, there exists a single
positive steady state, which is asymptotically stable. Here we describe an
algorithm for finding $WR_0$ realizations of polynomial dynamical systems,
whenever such realizations exist.
