A deficiency zero theorem for a class of power–law kinetic systems with non–reactant–determined interactions

College

College of Science

Department/Unit

Mathematics and Statistics Department

Document Type

Article

Source Title

Match

Volume

81

Issue

3

First Page

621

Last Page

638

Publication Date

1-1-2019

Abstract

The Deficiency Zero Theorem (DZT) provides definitive results about the dynamical behavior of chemical reaction networks with deficiency zero. Thus far, the available DZTs only apply to classes of power-law kinetic systems with reactant-determined interactions (i.e., the kinetic order vectors of the branching reactions of a reactant complex are identical). In this paper, we present the first DZT valid for a class of power-law systems with non-reactant-determined interactions (i.e., there are reactant complexes whose branching reactions have different kinetic order vectors). This class of power-law systems is characterized here by a decomposition into subnetworks with specific properties of their stoichiometric and reactant subspaces, as well as their kinetics. We illustrate our results to a power-law system of a pre-industrial carbon cycle model, from which we abstracted the properties of the above-mentioned decomposition. Specifically, our DZT is applied to a subnetwork of the carbon cycle system to describe the subnetwork’s steady states. It is also shown that the qualitative dynamical properties of the subnetwork may be lifted to the entire network of pre-industrial carbon cycle. © 2019 University of Kragujevac, Faculty of Science. All rights reserved.

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Disciplines

Physical Sciences and Mathematics

Keywords

Chemical kinetics; Carbon cycle (Biogeochemistry)

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