×

On multi-parametric bifurcations in a scalar piecewise-linear map. (English) Zbl 1087.37027

Summary: A one-dimensional piecewise-linear map is considered. The areas in the parameter space corresponding to specific periodic orbits are determined. Based on these results, it is shown that the structure of the 2D and 3D parameter spaces can be simply described using the concept of multiparametric bifurcations. It is demonstrated that an infinite number of two-parametric bifurcation lines starts at the origin of the 3D parameter space. Along each of these lines an infinite number of bifurcation planes starts, whereas the origin represents a three-parametric bifurcation.

MSC:

37E05 Dynamical systems involving maps of the interval
37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
PDFBibTeX XMLCite
Full Text: DOI Link