Bray-Liebhafsky oscillations

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.