Approximative classification of regions in parameter spaces of nonlinear ODEs yielding different qualitative behavior

Nonlinear dynamical systems can show a variety of different qualitative behaviors depending on the actual parameter values. As in many situations of practical relevance the parameter values are not precisely known it is crucial to determine the region in parameter space where the system exhibits the desired behavior. In this paper we propose a method to compute an approximative, analytical description of this region. Employing Markov-chain Monte-Carlo sampling, nonlinear support vector machines, and the novel notion of margin functions, an approximative classification function is determined. The properties of the method are illustrated by studying the dynamic behavior of the Higgins-Sel´kov oscillator.