# Attainable Regions of Dynamical Systems

## TL;DR

This paper defines and characterizes the attainable region of dynamical systems, especially in chemical kinetics, providing new mathematical insights and conjectures for specific classes of systems.

## Contribution

Introduces a formal definition of attainable regions for dynamical systems and extends the characterization to linear and certain weakly reversible systems.

## Key findings

- Characterized attainable regions for linear systems.
- Reported experiments and conjectures for weakly reversible systems.
- Adapted Vinzant's construction for convex hull faces of trajectories.

## Abstract

We present a mathematical definition for the attainable region of a dynamical system, with primary focus on mass action kinetics for chemical reactions. We characterise this region for linear dynamical systems, and we report on experiments and conjectures for weakly reversible systems with linkage class one. A construction due to Vinzant is adapted to give a representation of faces in the convex hull of trajectories.