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• W2096886711 abstract "In this paper 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." @default.
• W2096886711 created "2016-06-24" @default.
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• W2096886711 date "2006-07-13" @default.
• W2096886711 modified "2023-09-27" @default.
• W2096886711 title "Multi-parametric bifurcations in a piecewise–linear discontinuous map" @default.
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• W2096886711 doi "https://doi.org/10.1088/0951-7715/19/8/007" @default.
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