Canards in a Surface Oxidation Reaction

Canards are periodic orbits for which the trajectory follows both the attracting and repelling parts of a slow manifold. They are associated with a dramatic change in the amplitude and period of a periodic orbit within a very narrow interval of a control parameter. It is shown numerically that canards occur in an appropriate parameter range in twoand three-dimensional models of the platinum-catalyzed oxidation of carbon monoxide. By smoothly connecting associated stable and unstable manifolds in an asymptotic limit, we predict parameter values at which such canards exist. The relationship between the canards and saddle-loop bifurcations for these models is also demonstrated. Excellent agreement is found between the numerical and analytical results.