Slow-fast Bogdanov-Takens bifurcations (Q619877)

The paper deals with smooth families of slow-fast systems that represent a very general class of singular perturbation problems near a turning point. The authors introduce the notion of slow-fast Bogdanov-Takens bifurcation and provide a complete study of the perturbations from planar vector fields having a line of zeros, representing the singular limit of Bogdanov-Takens bifurcations. The bifurcation diagram is shown and the related phase portraits are given. Based on geometric singular perturbation theory, including blow-up technique, the authors obtain results that are valid on a uniform neighborhood both in parameter space and in the phase plane.