  It has long been known that complex balanced mass-action systems exhibit a
restrictive form of behaviour known as locally stable dynamics. This means that
within each compatibility class $\mathcal{C}_{\mathbf{x}_0}$---the forward
invariant space where solutions lies---there is exactly one equilibrium
concentration and that this concentration is locally asymptotically stable. It
has also been conjectured that this stability extends globally to
$\mathcal{C}_{\mathbf{x}_0}$. That is to say, all solutions originating in
$\mathcal{C}_{\mathbf{x}_0}$ approach the unique positive equilibrium
concentration rather than $\partial \mathcal{C}_{\mathbf{x}_0}$ or $\infty$. To
date, however, no general proof of this conjecture has been found.
  In this paper, we approach the problem of global stability for complex
balanced systems through the methodology of dividing the positive orthant into
regions called strata. This methodology has been previously applied to detailed
balanced systems---a proper subset of complex balanced systems---to show that,
within a stratum, trajectories are repelled from any face of $\mathbb{R}_{\geq
0}^m$ adjacent to the stratum. Several known global stability results for
detailed balanced systems are generalized to complex balanced systems.
