Reaction systems with complex chemistry give rise to complicated systems of nonlinear equations that don’t lend themselves to analytic solution. What’s more, increased complexity in the governing equations can give rise to complicated new phenomena that simple textbook reactors don’t admit. Even in the constant temperature case common in biology there can, for example, be unstable steady states, multiple steady states, sustained composition oscillations, and wild, chaotic dynamics.
Since each new network of chemical reactions gives rise to its own complicated system of differential equations, it becomes apparent that, in the absence of an overarching theory, we would be forced to study reaction systems on a case-by-case basis, and each new case would be fraught with terrible analytical difficulties. What’s needed is a way of looking at things from a broader and more general perspective.
That’s what Chemical Reaction Network Theory tries to do. The aim of the theory is to tie aspects of reaction network structure in a precise way to the kinds of dynamics the network might admit. A lot of progress has been made along these lines, but there is also much that remains unknown.
This website has resources both for those interested in the mathematics behind Chemical Reaction Network Theory and for those simply interested in seeing results that the theory delivers. For those that want to learn more about the underlying mathematics, Lectures on Chemical Reaction Networks provide a somewhat dated but nevertheless useful introduction. For those interested in seeing user-friendly computer implementation of the theory, The Chemical Reaction Network Toolbox provides means to make otherwise difficult deductions about reaction network behavior. More generally, there is an annotated bibliography of work with students and collaborators over the years. The bibliography is intended as a guide not only to work on reaction network theory but also to loosely related work on foundations of classical thermodynamics and the theory of reactor design.
The book "Foundations of Chemical Reaction Network Theory" was published by Springer in early 2019.