# K-variable kinetics

From Mathematics of Reaction Networks

A chemical reaction network is said to be endowed with **k-variable kinetics** if the kinetic vector has entries of the form

where is the stoichiometric vector for the reactant complex of the reaction and , for , for .

K-variable kinetics is a generalization of mass action kinetics which allows the rate of each reaction to vary within a compact region over time. The terminology "k-variable kinetics" was introduced by Gheorghe Craciun, Casian Pantea and Fedor Nazarov^{[1]} and has been further studied by Casian Pantea^{[2]} and David Anderson^{[3]}, who called the kinetics "bounded mass action kinetics".

## References

- ↑
Gheorghe Craciun, Casian Pantea, and Fedor Nazarov, Persistence and permanence of mass-action and power-law dynamical systems, to appear
*SIAM J. Appl. Math.*, 2012 - ↑ Casian Pantea, On the persistence and global stability of mass-action systems,
*SIAM J. Math. Anal.*, 44(3), 2012 - ↑ David Anderson, A proof of the global attractor conjecture in the single linkage class case,
*SIAM J. Appl. Math.*, 71(4):1487--1508, 2011