GEOMETRY OF MIXED-MODE OSCILLATIONS IN THE 3-D AUTOCATALATOR

We present a geometric explanation of a basic mechanism generating mix ed-mode oscillations in a prototypical simple model of a chemical osci llator. Our approach is based on geometric singular perturbation theor y and canard solutions. We explain how the small oscillations are gene rated near a special point, which is classified as a folded saddle-nod e for the reduced problem. The canard solution passing through this po int separates small oscillations from large relaxation type oscillatio ns. This allows to define a one-dimensional return map in a natural wa y. This bimodal map is capable of explaining the observed bifurcation sequence convincingly.