A methodology for designing experiments aimed at determining the set of limit points in a bistable system is developed and applied, in an automated system, to nonisothermal oxidation of ethylene on platinum. Bifurcation diagrams are automatically traced by fine-scanning domains that were identified to include limit points in the preceding coarse scan. Model discrimination shows that a Langmuir-Hinshelwood rate expression may account for the observed qualitative features. The parameter estimation procedure is aimed at fitting the limit points by identifying and locating singular points and special features of this set. We derive the defining conditions and search for parameters that satisfy them within the uncertainty of the experimental data. Good description of the bifurcation diagrams and sets is achieved with few parameters.