Remerging Feigenbaum trees in dynamical systems

Martin Bier, Tassos C. Bountis

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128 Citations (Scopus)

Abstract

Finite sequences of remerging period-doubling bifurcations have been recently observed in a variety of physically interesting dynamical systems. We show here that such remerging Feigenbaum trees are quite common in models with more than one parameter and discuss a number of criteria under which they are generally observed. These criteria are applied to simple mappings as well as the conservative Duffing's equation where the formation of a primary "bubble" is seen to lead to higher-order bubbles and hence to remerging Feigenbaum sequences. In the case of Duffing's equation, we follow the development of one such sequence, with the aid of the variation of the winding number along a symmetry axis of the problem.

Original languageEnglish
Pages (from-to)239-244
Number of pages6
JournalPhysics Letters A
Volume104
Issue number5
DOIs
Publication statusPublished - Sep 3 1984

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ASJC Scopus subject areas

  • Physics and Astronomy(all)

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