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Journal of Nonlinear Science

, Volume 10, Issue 1, pp 133–144 | Cite as

Bray—Liebhafsky Oscillations

  • W. R. Derrick
  • L. V. Kalachev
Article

Summary.

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.

Keywords

Hopf Bifurcation Homoclinic Orbit Homoclinic Bifurcation Hopf Bifurcation Point Stable Focus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 2000

Authors and Affiliations

  • W. R. Derrick
    • 1
  • L. V. Kalachev
    • 1
  1. 1.University of Montana, Missoula, MT 59812, USAUSA

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