Geodesic
Forward-Invariant Peeling in Chemical Dynamics: a Simple Case Study
A. N. Gorban1
1 Department of Mathematics, University of Leicester, Leicester, LE1 7RH, UK
Mathematical modelling of natural phenomena, Tome 10 (2015) no. 5, pp. 126-134

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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 ≤ 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 : 10.1051/mmnp/201510509

A. N. Gorban 1

1 Department of Mathematics, University of Leicester, Leicester, LE1 7RH, UK 
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A. N. Gorban. Forward-Invariant Peeling in Chemical Dynamics: a Simple Case Study. Mathematical modelling of natural phenomena, Tome 10 (2015) no. 5, pp. 126-134. doi: 10.1051/mmnp/201510509

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