Oregonator: General results of positive steady state and its stability (Q1814851)

Consider the differential equations \((*)\) \(\varepsilon dx/dt= x(1-x)- fz\frac{x-\mu}{x+\mu}\), \(dz/dt=x-z\) representing a two-dimensional version due to J. J. Tyson of the Oregonator model for the famous Belousov-Zhabotinskii reaction. For \(0<\mu<1\), \(0<\varepsilon<1\), \(0<f<+\infty\), the author studies the stability of the unique positive equilibrium of \((*)\) and establishes Hopf bifurcation.