Algorithmic Contributions to the Qualitative Analysis

This thesis deals with algorithmic local and global techniques in the qualitative analysis of autonomous parametric dynamical systems. Specifically, algorithms for symbolic parametric investigations of the existence of limit cycles are developed and investigated and applied to several applications, especially from life science informatics.In order to investigate the global question of the absence of oscillations some generalizations of the classical Bendixson-Dulac criterion, which is asufficient criterion for the exclusion of limit cycles only, to higher dimensions are made algorithmic.