On Global Stability of the Lotka Reactions with Generalized Mass-Action Kinetics

Chemical reaction networks with generalized mass-action kinetics lead to power-law dynamical systems. As a simple example, we consider the Lotka reactions with two chemical species and arbitrary power-law kinetics. We study existence, uniqueness, and stability of the positive equilibrium, in particu...

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Veröffentlicht in:	Acta applicandae mathematicae 2017-10, Vol.151 (1), p.53-80
Hauptverfasser:	Boros, Balázs, Hofbauer, Josef, Müller, Stefan
Format:	Artikel
Sprache:	eng
Schlagworte:	Applications of Mathematics Asymptotic properties Calculus of Variations and Optimal Control Optimization Chemical reactions Computational Mathematics and Numerical Analysis Kinetics Mathematics Mathematics and Statistics Partial Differential Equations Probability Theory and Stochastic Processes Reaction kinetics Stability Uniqueness
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Beschreibung
Zusammenfassung:	Chemical reaction networks with generalized mass-action kinetics lead to power-law dynamical systems. As a simple example, we consider the Lotka reactions with two chemical species and arbitrary power-law kinetics. We study existence, uniqueness, and stability of the positive equilibrium, in particular, we characterize its global asymptotic stability in terms of the kinetic orders.
ISSN:	0167-8019 1572-9036
DOI:	10.1007/s10440-017-0102-9