Issue |
Math. Model. Nat. Phenom.
Volume 10, Number 5, 2015
Dynamics of Chemical Reaction Networks
|
|
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Page(s) | 126 - 134 | |
DOI | https://doi.org/10.1051/mmnp/201510509 | |
Published online | 27 August 2015 |
Forward-Invariant Peeling in Chemical Dynamics: a Simple Case Study
Department of Mathematics, University of
Leicester, Leicester,
LE1 7RH,
UK
⋆
Corresponding author. E-mail: ag153@le.ac.uk
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 → ∞).
Mathematics Subject Classification: 37C10 / 34D20 / 93D05
Key words: chemical kinetics / Lyapunov function / persistence
© EDP Sciences, 2015
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