K-variable kinetics

A chemical reaction network ${\mathcal {N}}=({\mathcal {S}},{\mathcal {C}},{\mathcal {R}})$ is said to be endowed with k-variable kinetics if the kinetic vector ${\vec {R}}(t,{\vec {c}})$ has entries of the form

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{R}_i(t,\vec{c}) = k_i(t) c_1^{y_{1i}} \cdots c_n^{y_{ni}}, \; \; \; i = 1, \ldots, r, }

where ${\vec {y}}_{i}=[y_{1i},\ldots ,y_{ni}]^{T}$ is the stoichiometric vector for the reactant complex of the $i^{th}$ reaction and $1/\eta <k_{i}(t)<\eta$, for $i=1,\ldots ,n$, for $\eta >0$.

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 and has been further studied by Casian Pantea and David Anderson, who called the kinetics "bounded mass action kinetics".