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PERIOD-DOUBLING SCENARIO WITHOUT FLIP BIFURCATIONS IN A ONE-DIMENSIONAL MAP

Institute of Parallel and Distributed Systems (IPVS), University of Stuttgart, Universitätstrasse 38, D-70569 Stuttgart, Germany

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and

M. SCHANZ

Institute of Parallel and Distributed Systems (IPVS), University of Stuttgart, Universitätstrasse 38, D-70569 Stuttgart, Germany

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https://doi.org/10.1142/S0218127405012752Cited by:13 (Source: Crossref)

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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