Limit-cycle behaviour in a model chemical reaction: the cubic autocatalator

Limit cycles are sought in a mathematical model of a simple hypothetical chemical reaction involving essentially only two reacting species. Physically, these limit cycles correspond to time-periodic oscillations in the concentrations of the two chemicals. A combination of analytical and numerical methods reveals that limit-cycle behaviour is only possible in a restricted region of the parameter space. Strong numerical evidence is presented to assert that the limit cycle is unique and stable to infinitesimal perturbations. Numerical solutions are displayed and discussed.