Bifurcation problems with high codimensions

Many biological systems can be modeled by autonomous ordinary differential equations. An important question is how the model behaves at a nonhyperbolic singularity locally. The possible behaviour can be described by the versai deformation of the singularity. In this paper, a classification of the Takens-Bogdanov singularities is presented, and some property of two singularities of higher codimension is proved. Lastly, we illustrate the investigation of singularities on a simple chemical model. The model is of biological interest and it turns out to have a complex dynamic behaviour.