# Endotactic Networks and Toric Differential Inclusions

## TL;DR

This paper demonstrates that endotactic networks, a broad class of biological interaction networks, can be embedded into toric differential inclusions, extending previous work on weakly reversible networks and contributing to the understanding of persistence.

## Contribution

It shows that endotactic networks, larger than weakly reversible ones, can be embedded into toric differential inclusions, advancing the study of network persistence.

## Key findings

- Endotactic networks can be embedded into toric differential inclusions.
- Endotactic networks form the largest class with this embedding property.
- Supports the conjecture relating network structure to persistence.

## Abstract

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.