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


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.


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



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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© 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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