Mathematical analysis of chemical reaction systems
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 …
long history, and involves many types of models: deterministic versus stochastic, continuous …
Foundations of chemical reaction network theory
M Feinberg - 2019 - Springer
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 …
Principia. I do this for a number of reasons, not least of which is the connection I hope they …
Sign conditions for injectivity of generalized polynomial maps with applications to chemical reaction networks and real algebraic geometry
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 …
families of polynomial maps with arbitrary real exponents defined on the positive orthant …
Toric differential inclusions and a proof of the global attractor conjecture
G Craciun - arXiv preprint arXiv:1501.02860, 2015 - arxiv.org
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 …
dynamical systems on the positive orthant) have a globally attracting point within each …
Generalized mass action systems: Complex balancing equilibria and sign vectors of the stoichiometric and kinetic-order subspaces
S Muller, G Regensburger - SIAM Journal on Applied Mathematics, 2012 - SIAM
Mass action systems capture chemical reaction networks in homogeneous and dilute
solutions. We suggest a notion of generalized mass action systems that admits arbitrary …
solutions. We suggest a notion of generalized mass action systems that admits arbitrary …
Concordant chemical reaction networks
G Shinar, M Feinberg - Mathematical biosciences, 2012 - Elsevier
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 …
structural property called concordance. We show that the class of concordant networks …
On the persistence and global stability of mass-action systems
C Pantea - SIAM Journal on Mathematical Analysis, 2012 - SIAM
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 …
chemical reaction systems, modeled by deterministic mass-action kinetics. We approach two …
New approach to the stability of chemical reaction networks: Piecewise linear in rates Lyapunov functions
MA Al-Radhawi, D Angeli - IEEE Transactions on Automatic …, 2015 - ieeexplore.ieee.org
Piecewise-linear in rates (PWLR) Lyapunov functions are introduced for a class of chemical
reaction networks (CRNs). In addition to their simple structure, these functions are robust …
reaction networks (CRNs). In addition to their simple structure, these functions are robust …
The inheritance of nondegenerate multistationarity in chemical reaction networks
We study how the properties of allowing multiple positive nondegenerate equilibria (MPNE)
and multiple positive linearly stable equilibria (MPSE) are inherited in chemical reaction …
and multiple positive linearly stable equilibria (MPSE) are inherited in chemical reaction …
Graph-theoretic criteria for injectivity and unique equilibria in general chemical reaction systems
In this paper we discuss the question of how to decide when a general chemical reaction
system is incapable of admitting multiple equilibria, regardless of parameter values such as …
system is incapable of admitting multiple equilibria, regardless of parameter values such as …