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 …

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

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 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 …

Neurons in the brain represent external stimuli via neural codes. These codes often arise
from stereotyped stimulus-response maps, associating to each neuron a convex receptive …

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 …

Many dynamical systems arising in biology and other areas exhibit multistationarity (two or
more positive steady states with the same conserved quantities). Although deciding …

Switch-like responses arising from bistability have been linked to cell signaling processes
and memory. Revealing the shape and properties of the set of parameters that lead to …

Steady-state analysis of dynamical systems for biological networks gives rise to algebraic
varieties in high-dimensional spaces whose study is of interest in their own right. We …

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 …