A deficiency-one algorithm for power-law kinetic systems with reactant-determined interactions

College

College of Science

Department/Unit

Mathematics and Statistics Department

Document Type

Article

Source Title

Journal of Mathematical Chemistry

Volume

56

Issue

10

First Page

2929

Last Page

2962

Publication Date

11-1-2018

Abstract

This paper addresses the problem of determining the capacity of a deficiency-one network, endowed with rate laws more general than mass action kinetics, to admit multiple positive steady states—that is, whether there exist rate constants such that the corresponding differential equations admit two distinct stoichiometrically compatible steady states where all concentrations are positive. We extend the Deficiency-One Algorithm of M. Feinberg to deal with PL-RDK systems, which are kinetic systems with power-law rate functions whose kinetic orders are identical for reactions with the same reactant complex. The algorithm is applied to a power-law approximation of the Earth’s pre-industrial carbon cycle model, which gave the original motivation for our study. © 2018, Springer International Publishing AG, part of Springer Nature.

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Digitial Object Identifier (DOI)

10.1007/s10910-018-0925-2

Disciplines

Chemistry | Mathematics

Keywords

Carbon cycle (Biogeochemistry); Chemical kinetics; Equilibrium

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