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Acta Applicandae Mathematicae

, Volume 151, Issue 1, pp 53–80 | Cite as

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

  • Balázs Boros
  • Josef Hofbauer
  • Stefan MüllerEmail author
Article

Abstract

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.

Keywords

Chemical reaction network Power-law kinetics Andronov-Hopf bifurcation Dulac function 

Notes

Acknowledgements

We thank Georg Regensburger, Valerij Romanovskij, and János Tóth for fruitful discussions. BB and SM were supported by the Austrian Science Fund (FWF), project P28406.

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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Radon Institute for Computational and Applied MathematicsAustrian Academy of SciencesLinzAustria
  2. 2.Faculty of MathematicsUniversity of ViennaViennaAustria

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