Endotactic Networks and Toric Differential Inclusions

An important dynamical property of biological interaction networks is persistence, which intuitively means that "no species goes extinct". It has been conjectured that dynamical system models of weakly reversible networks (i.e., networks for which each reaction is part of a cycle) are persistent. The property of persistence is also related to the well known global attractor conjecture. An approach for the proof of the global attractor conjecture uses an embedding of weakly reversible dynamical systems into toric differential inclusions. We show that the larger class of endotactic dynamical systems can also be embedded into toric differential inclusions. Moreover, we show that, essentially, endotactic networks form the largest class of networks with this property.