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Title: Forward-Invariant Peeling in Chemical Dynamics: a Simple Case Study
Authors: Gorban, A. N.
First Published: 27-Aug-2015
Publisher: EDP Sciences, Cambridge University Press (CUP)
Citation: Mathematical Modelling of Natural Phenomena, 2015, 10 (5), pp. 126-134 (9)
Abstract: Forward-invariant peeling aims to produce forward-invariant subset from a given set in phase space. The structure of chemical kinetic equations allows us to describe the general operations of the forward-invariant peeling. For example, we study a simple reaction network with three components A1,A2,A3 and reactions A1 → A2 → A3 → A1, 2A1 ⇌ 3A2 (without any stoichiometric conservation law). We assume that kinetics obey the classical mass action law and reaction rate constants are positive intervals 0 <ki min ≤ ki ≤ ki max< ∞. Kinetics of this system is described by a system of differential inclusions. We produce forward-invariant sets for these kinetic inclusions from the sets { c | ci ≥ 0, ∑ ci ≥ ε } by the forward-invariant peeling (for sufficiently small ε> 0). In particular, this construction proves persistence of this kinetic system (a positive solution cannot approach the origin even asymptotically, as t → ∞).
DOI Link: 10.1051/mmnp/201510509
ISSN: 0973-5348
eISSN: 1760-6101
Version: Publisher Version
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © 2015, EDP Sciences, Cambridge University Press (CUP). Deposited with reference to the publisher’s open access archiving policy.
Description: Mathematics Subject Classification: 37C10, 34D20, 93D05
Appears in Collections:Published Articles, Dept. of Mathematics

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