Bibliography | Avrutin, Viktor; Schanz, Michael; Banerjee, Soumitro: Multi-parametric Bifurcations in a piecewise-linear discontinuous Map. In: Nonlinearity. Vol. 19. University of Stuttgart, Faculty of Computer Science, Electrical Engineering, and Information Technology. pp. 1875-1906, english. IoP The Institute of Physics Publishing, March 2006. DOI: 10.1088/0951-7715/19/8/007. Article in Journal.
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CR-Schema | G.1.0 (Numerical Analysis General) J.2 (Physical Sciences and Engineering)
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Keywords | codimension-3; non-smooth dynamical systems; period adding; period increment |
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.
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Contact | Michael.Schanz@informatik.uni-stuttgart.de Viktor.Avrutin@informatik.uni-stuttgart.de |
Department(s) | University of Stuttgart, Institute of Parallel and Distributed Systems, Image Understanding
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Project(s) | AnT
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Entry date | August 9, 2006 |
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