Avrutin, Viktor; Schanz, Michael; Banerjee, Soumitro Multi-parametric bifurcations in a piecewise-linear discontinuous map. (English) Zbl 1190.37042 Nonlinearity 19, No. 8, 1875-1906 (2006). Summary: A one-dimensional piecewise linear map with discontinuous system function is investigated. This map actually represents the normal form of the discrete-time representation of many practical systems in the neighbourhood of the point of discontinuity. In the 3D parameter space of this system we detect an infinite number of co-dimension one bifurcation planes, which meet along an infinite number of co-dimension two bifurcation curves. Furthermore, these curves meet at a few co-dimension three bifurcation points. Therefore, the investigation of the complete structure of the 3D parameter space can be reduced to the investigation of these co-dimension three bifurcations, which turn out to be of a generic type. Tracking the influence of these bifurcations, we explain a broad spectrum of bifurcation scenarios (like period increment and period adding) which are observed under variation of one control parameter. Additionally, the bifurcation structures which are induced by so-called big bang bifurcations and can be observed by variation of two control parameters can be explained. Cited in 39 Documents MSC: 37E05 Dynamical systems involving maps of the interval 37G05 Normal forms for dynamical systems 37G99 Local and nonlocal bifurcation theory for dynamical systems PDFBibTeX XMLCite \textit{V. Avrutin} et al., Nonlinearity 19, No. 8, 1875--1906 (2006; Zbl 1190.37042) Full Text: DOI