Journal of Nonlinear Science

, Volume 10, Issue 1, pp 133–144

Bray—Liebhafsky Oscillations


  • W. R. Derrick
    • University of Montana, Missoula, MT 59812, USA
  • L. V. Kalachev
    • University of Montana, Missoula, MT 59812, USA

DOI: 10.1007/s003329910006

Cite this article as:
Derrick, W. & Kalachev, L. J. Nonlinear Sci. (2000) 10: 133. doi:10.1007/s003329910006


A system describing an oscillating chemical reaction (known as a Bray—Liebhafsky oscillating reaction) is considered. It is shown that large amplitude oscillations arise through a homoclinic bifurcation and vanish through a subcritical Hopf bifurcation. An approximate locus of points corresponding to the homoclinic orbit in a parameter space is calculated using a variation of the Bogdanov—Takens—Carr method. A special feature of the problem is related to the fact that nonlinear terms in the equations contain square and cubic roots of expressions depending on the unknowns. For a particular model considered it is possible to obtain most of the results analytically.

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© Springer-Verlag New York Inc. 2000