Analysis of chemical kinetic systems over the entire parameter space IV. The Sal'nikov oscillator with two temperature-dependent reaction rates

This paper investigates a model chemical reaction in which a substance undergoes a two-stage decay, each stage exhibiting Arrhenius temperature dependence. The system is assumed to be well stirred so it is described by two highly nonlinear ordinary differential equations containing four parameters. Degenerate bifurcation theory and numerical analysis are used to investigate the behaviour of the system over the whole of physical parameter space. A large number of degenerate bifurcations are identified and located and the system is shown to exhibit 16 qualitatively different phase portraits. Degeneracies of higher codimension than would be expected occur in this system giving rise to some highly non-uniform behaviour both in phase and parameter space. This behaviour seems to be generic in thermokinetic systems with more than one Arrhenius nonlinearity.