We present some simple mass-action systems with limit cycles that fall under the scope of
the Deficiency-One Theorem. All the constructed examples are mass-conserving and their …

The induced kinetic differential equation of a reaction network endowed with mass action
type kinetics is a system of polynomial differential equations. The problem studied here is …

Systems of differential equations with polynomial right-hand sides are very common in
applications. On the other hand, their mathematical analysis is very challenging in general …

Abstract Systems of differential equations with polynomial right-hand sides are very common
in applications. In particular, when restricted to the positive orthant, they appear naturally …

An important dynamical property of biological interaction networks is persistence, which
intuitively means that “no species goes extinct." It has been conjectured that dynamical …

We discuss three examples of bimolecular mass-action systems with three species, due to
Feinberg, Berner, Heinrich, and Wilhelm. Each system has a unique positive equilibrium …

Under the assumption of mass-action kinetics, a dynamical system may be induced by
several different reaction networks and/or parameters. It is therefore possible for a mass …

Polynomial dynamical systems (ie, dynamical systems with polynomial right-hand side) are
ubiquitous in applications, especially as models of reaction networks and interaction …

We show that weakly reversible mass-action systems can have a continuum of positive
steady states, coming from the zeroes of a multivariate polynomial. Moreover, the same is …

Under mass-action kinetics, complex-balanced systems emerge from biochemical reaction
networks and exhibit stable and predictable dynamics. For a reaction network $ G $, the …