Journal of Mathematical Chemistry

, Volume 19, Issue 2, pp 111–130

Mathematical analysis of the smallest chemical reaction system with Hopf bifurcation

  • Thomas Wilhelm
  • Reinhart Heinrich

DOI: 10.1007/BF01165179

Cite this article as:
Wilhelm, T. & Heinrich, R. J Math Chem (1996) 19: 111. doi:10.1007/BF01165179


Recently we presented an up to now unstudied three-dimensional dynamical system which is, according to our given definition, the smallest chemical reaction system with Hopf bifurcation. We here study the Hopf bifurcation in detail and prove that near the bifurcation point a stable limit cycle arises. In the analysis we use the methods of local bifurcation theory, especially the center manifold and the normal form theorem. In a similar way we analyse the also occurring transcritical bifurcation. Besides studying local stability, we give the proofs for global stability of the trivial steady state in the whole positive phase space and for the nontrivial steady state in a closed domain containing the steady state point.

Copyright information

© J.C. Baltzer AG, Science Publishers 1996

Authors and Affiliations

  • Thomas Wilhelm
    • 1
  • Reinhart Heinrich
    • 1
  1. 1.Institut für Biologie, Theoretische BiophysikHumboldt- Universität zu BerlinBerlinGermany

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