  Some of the most common mathematical models in biology, chemistry, physics,
and engineering, are polynomial dynamical systems, i.e., systems of
differential equations with polynomial right-hand sides. Inspired by notions
and results that have been developed for the analysis of reaction networks in
biochemistry and chemical engineering, we show that any polynomial dynamical
system on the positive orthant $\mathbb R^n_{> 0}$ can be regarded as being
generated by an oriented graph embedded in $\mathbb R^n$, called
$\mathit{Euclidean \ embedded \ graph}$. This allows us to recast key
conjectures about reaction network models (such as the Global Attractor
Conjecture, or the Persistence Conjecture) into more general versions about
some important classes of polynomial dynamical systems. Then, we introduce
$\mathit{toric \ differential \ inclusions}$, which are piecewise constant
autonomous dynamical systems with a remarkable geometric structure. We show
that if a Euclidean embedded graph $G$ has some reversibility properties, then
any polynomial dynamical system generated by $G$ can be embedded into a toric
differential inclusion. We discuss how this embedding suggests an approach for
the proof of the Global Attractor Conjecture and Persistence Conjecture.
