Bray-Liebhafsky oscillations (Q1583864)

Consider the differential system (*) \(dx/dt= x^{2/3}- \sqrt xy\), \(dy/dt= x^{1/3}-\sigma (y-\delta)\) describing an oscillating chemical reaction. The authors study the bifurcation diagram of (*) in the \(\sigma, \delta\)-plane analytically and numerically. It is shown that large amplitude oscillations arise through a homoclinic bifurcation and vanish through a subcritical Hopf bifurcation.