The algebra of reaction network models

Reaction networks (i.e., oriented graphs embedded in Euclidean space) give rise to systems of differential equations with polynomial right-hand side. In general, such systems are very difficult to analyze. For example, they can give rise to questions related to Hilbert’s 16th problem, the Jacobian conjecture, or chaotic dynamics.

We will discuss algebraic approaches for analyzing dynamical properties of reaction network models, inspired by intuition from chemistry and thermodynamics.