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 …

Nonlinear algebra provides modern mathematical tools to address challenges arising in the
sciences and engineering. It is useful everywhere, where polynomials appear: in particular …

This book, as with others in the series, is intended to provide supplementary material for
courses in probability or stochastic processes. The mathematical focus is on counting …

This paper is concerned with the dynamical properties of deterministically modeled chemical
reaction systems. Specifically, this paper provides a proof of the Global Attractor Conjecture …

In this paper and Paper II, we outline a general framework for the thermodynamic description
of open chemical reaction networks, with special regard to metabolic networks regulating …

Cellular physiology is implemented by formidably complex biochemical systems with highly
nonlinear dynamics, presenting a challenge for both experiment and theory. Time-scale …

Mass-action chemical reaction systems are frequently used in computational biology. The
corresponding polynomial dynamical systems are often large (consisting of tens or even …

Our paper reviews some key concepts in chemical reaction network theory and
mathematical epidemiology, and examines their intersection, with three goals. The first is to …

Persistence and permanence are properties of dynamical systems that describe the long-
term behavior of the solutions and in particular specify whether positive solutions approach …

The long-term behaviors of biochemical systems are often described by their steady states.
Deriving these states directly for complex networks arising from real-world applications …