157 citations · 2.9k across the 96 of their papers we have counts for
6 papers · 1 filter
Transition states and entangled mass action law
Alexander N. Gorban
The classical approaches to the derivation of the (generalized) Mass Action Law (MAL) assume that the intermediate transition state (i) has short life time and (ii) is in partial e…
New universal Lyapunov functions for non-linear reaction networks
A. N. Gorban
In 1961, Rényi discovered a rich family of non-classical Lyapunov functions for kinetics of the Markov chains, or, what is the same, for the linear kinetic equations. This family w…
Model reduction in chemical dynamics: slow invariant manifolds, singular perturbations, thermodynamic estimates, and analysis of reaction graph
A. N. Gorban
The paper has two goals: It presents basic ideas, notions, and methods for reduction of reaction kinetics models: quasi-steady-state, quasi-equilibrium, slow invariant manifolds, a…
Generalized Mass Action Law and Thermodynamics of Nonlinear Markov Processes
A. N. Gorban, V. N. Kolokoltsov
The nonlinear Markov processes are the measure-valued dynamical systems which preserve positivity. They can be represented as the law of large numbers limits of general Markov mode…
The Michaelis-Menten-Stueckelberg Theorem
A. N. Gorban, M. Shahzad
We study chemical reactions with complex mechanisms under two assumptions: (i) intermediates are present in small amounts (this is the quasi-steady-state hypothesis or QSS) and (ii…
Asymptotology of Chemical Reaction Networks
A. N. Gorban, O. Radulescu, A. Y. Zinovyev
The concept of the limiting step is extended to the asymptotology of multiscale reaction networks. Complete theory for linear networks with well separated reaction rate constants i…