  The use of mathematical methods for the analysis of chemical reaction systems
has a very long history, and involves many types of models: deterministic
versus stochastic, continuous versus discrete, and homogeneous versus spatially
distributed. Here we focus on mathematical models based on deterministic
mass-action kinetics. These models are systems of coupled nonlinear
differential equations on the positive orthant. We explain how mathematical
properties of the solutions of mass-action systems are strongly related to key
properties of the networks of chemical reactions that generate them, such as
specific versions of reversibility and feedback interactions.
