Computing Convex Hulls of Trajectories

TL;DR

This paper develops numerical algorithms to compute convex hulls of trajectories in polynomial dynamical systems, aiding in analyzing attainable regions in chemical reaction networks.

Contribution

It introduces new numerical methods for identifying the stratified faces of convex hulls of polynomial trajectories, with an implementation using Bensolve Tools.

Findings

Algorithms successfully identify convex hull faces of polynomial trajectories.

Implementation demonstrates practical utility in chemical reaction network analysis.

Provides a computational step for studying attainable regions.

Abstract

We study the convex hulls of trajectories of polynomial dynamical systems. Such trajectories include real algebraic curves. The boundaries of the resulting convex bodies are stratified into families of faces. We present numerical algorithms for identifying these patches. An implementation based on the software Bensolve Tools is given. This furnishes a key step in computing attainable regions of chemical reaction networks.