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 …

When I am called upon to teach fluid mechanics, I always show students a copy of Newton's
Principia. I do this for a number of reasons, not least of which is the connection I hope they …

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 …

Mathematical modelling has become an established tool for studying the dynamics of
biological systems. Current applications range from building models that reproduce …

The global attractor conjecture says that toric dynamical systems (ie, a class of polynomial
dynamical systems on the positive orthant) have a globally attracting point within each …

This paper introduces the class of strongly endotactic networks, a subclass of the endotactic
networks introduced by Craciun, Nazarov, and Pantea. The main result states that the global …

The quantitative convergence to equilibrium for reaction-diffusion systems arising from
complex balanced chemical reaction networks with mass action kinetics is studied using the …

This paper concerns the long-term behavior of population systems, and in particular of
chemical reaction systems, modeled by deterministic mass-action kinetics. We approach two …

I revisit two theories of cell differentiation in multicellular organisms published a half-century
ago, Stuart Kauffman's global genome regulatory dynamics (GGRD) model and Roy Britten's …

Some of the most common mathematical models in biology, chemistry, physics, and
engineering are polynomial dynamical systems, ie, systems of differential equations with …