Bibliography | Avrutin, Viktor; Schanz, Michael: Period-doubling Scenario without Flip Bifurcations in a one-dimensional Map. In: International Journal of Bifurcation and Chaos. Vol. 15(4). University of Stuttgart, Faculty of Computer Science, Electrical Engineering, and Information Technology. pp. 1267-1284, english. World Scientific Publishing Company, April 2005. DOI: 10.1142/S0218127405012752. Article in Journal.
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CR-Schema | G.1.10 (Numerical Analysis Applications) J.2 (Physical Sciences and Engineering)
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Keywords | Period-doubling; border collision; piecewise-smooth vector field; kneading orbits |
Abstract | In this work a one-dimensional piecewise-smooth dynamical system, representing a Poincaré return map for dynamical systems of the Lorenz type, is investigated. The system shows a bifurcation scenario similar to the classical period-doubling one, but which is influenced by so-called border collision phenomena and denoted as border collision period-doubling bifurcation scenario. This scenario is formed by a sequence of pairs of bifurcations, whereby each pair consists of a border collision bifurcation and a pitchfork bifurcation. The mechanism leading to this scenario and its characteristic properties, like symmetry-breaking and symmetry-recovering as well as emergence of coexisting attractors, are investigated.
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Copyright | World Scientific Publishing Company |
Contact | Michael.Schanz@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 | October 17, 2005 |
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