A reaction network is a graph in which the nodes and edges describe interactions between biochemical species (molecules). The concentrations of the species are often modeled by ordinary differential equations, where the kinetics of the vector fields are governed by the reaction graph. One of the main goals of researchers studying biological systems is to characterize network structures that induce characteristic behaviors of the corresponding dynamical system.

In this talk, we will first discuss milestone results in this field. We will then introduce recent results on connections between reaction network theory and reaction–diffusion systems. In particular, we provide a topological condition on a reaction network that guarantees global existence of the corresponding reaction–diffusion system.