Bibliography | Schenke, Björn; Avrutin, Viktor; Schanz, Michael: On a bifurcation structure mimicking period adding. In: Proceedings of the Royal Society A. Vol. 467(2129). University of Stuttgart, Faculty of Computer Science, Electrical Engineering, and Information Technology. pp. 1503-1518, english. London: The Royal Society, May 8, 2011. DOI: 10.1098/rspa.2010.0573. Article in Journal.
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CR-Schema | J.2 (Physical Sciences and Engineering) G.2 (Discrete Mathematics)
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Keywords | piecewise smooth systems; border collision bifurcations; simple limiter control; nested period-incrementing bifurcation scenario |
Abstract | In this work, we investigate a piecewise-linear discontinuous scalar map defined on three partitions. This map is specifically constructed in such a way that it shows a recently discovered bifurcation scenario in its pure form. Owing to its structure on the one hand and the similarities to the nested period-adding scenario on the other hand, we denoted the new bifurcation scenario as nested period-incrementing bifurcation scenario. The new bifurcation scenario occurs in several physical and electronical systems but usually not isolated, which makes the description complicated. By isolating the scenario and using a suitable symbolic description for the asymptotically stable periodic orbits, we derive a set of rules in the space of symbolic sequences that explain the structure of the stable periodic domain in the parameter space entirely. Hence, the presented work is a necessary step for the understanding of the more complicated bifurcation scenarios mentioned above.
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Full text and other links | Online
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Contact | E-Mail: Bjoern.Schenke@ipvs.uni-stuttgart.de |
Department(s) | University of Stuttgart, Institute of Parallel and Distributed Systems, Image Understanding
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Project(s) | AnT, OCiND
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Entry date | May 25, 2011 |
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