Avrutin, Viktor ; Schanz, Michael ; Banerjee, Soumitro (2006) Multi-parametric bifurcations in a piecewise-linear discontinuous map Nonlinearity, 19 (8). pp. 1875-1906. ISSN 0951-7715
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Official URL: http://iopscience.iop.org/0951-7715/19/8/007
Related URL: http://dx.doi.org/10.1088/0951-7715/19/8/007
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.
Item Type: | Article |
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Source: | Copyright of this article belongs to Institute of Physics Publishing. |
ID Code: | 21403 |
Deposited On: | 20 Nov 2010 12:57 |
Last Modified: | 17 May 2016 05:37 |
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