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 …

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 …

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

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

Chemical reaction systems are dynamical systems that arise in chemical engineering and
systems biology. In this work, we consider the question of whether the minimal (in a precise …

We study how the properties of allowing multiple positive nondegenerate equilibria (MPNE)
and multiple positive linearly stable equilibria (MPSE) are inherited in chemical reaction …

We extend previous work on injectivity in chemical reaction networks to general interaction
networks. Matrix-and graph-theoretic conditions for injectivity of these systems are …

The goal of this paper is to gather and develop some necessary and sufficient criteria for
injectivity and multistationarity in vector fields associated with a chemical reaction network …

Multistationarity in molecular systems underlies switch-like responses in cellular decision
making. Determining whether and when a system displays multistationarity is in general a …