Forward-Invariant Peeling in Chemical Dynamics: a Simple Case Study

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,A...

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Bibliographic Details
Published in:Mathematical modelling of natural phenomena 2015-01, Vol.10 (5), p.126-134
Main Author: Gorban, A. N.
Format: Article
Language:English
Subjects:
34D20
37C10
93D05
Case studies
chemical kinetics
Inclusions
Invariants
Kinetic equations
Kinetics
Lyapunov function
Organic chemistry
Peeling
persistence
Rate constants
Reaction kinetics
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Summary: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 0). In particular, this construction proves persistence of this kinetic system (a positive solution cannot approach the origin even asymptotically, as t → ∞).
ISSN:0973-5348
1760-6101
DOI:10.1051/mmnp/201510509