Some criticism concerning the Brusselator model of an oscillating chemical reaction

The Brusselator is well known to exhibit an instability of the Hopf-bifurcation type leading to the appearance of limit-cycle oscillations. Here we show that this behaviour disappears entirely when detailed balancing and conservation of mass are strictly applied. Violation of both of these principles simultaneously is necessary for the instability. We conclude that the Brusselator, in spite of its termolecular autocatalytic step, is not an acceptable oscillatory model because it violates both detailed balance and conservation of mass. Computer simulations confirm the conclusions reached analytically.