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 …

Reaction networks, or equivalently Petri nets, are a general framework for describing
processes in which entities of various kinds interact and turn into other entities. In chemistry …

Which reaction networks, when taken with mass-action kinetics, have the capacity for
multiple steady states? There is no complete answer to this question, but over the last 40 …

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

We give necessary and sufficient conditions in terms of sign vectors for the injectivity of
families of polynomial maps with arbitrary real exponents defined on the positive orthant …

Mass action systems capture chemical reaction networks in homogeneous and dilute
solutions. We suggest a notion of generalized mass action systems that admits arbitrary …

In biochemical networks, complex dynamical features such as superlinear growth and
oscillations are classically considered a consequence of autocatalysis. For the large class of …

We describe a large class of chemical reaction networks, those endowed with a subtle
structural property called concordance. We show that the class of concordant networks …

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 …

Bistability has important implications in signaling pathways, since it indicates a potential cell
decision between alternative outcomes. We present two approaches developed in the …