BCSSS

International Encyclopedia of Systems and Cybernetics

2nd Edition, as published by Charles François 2004 Presented by the Bertalanffy Center for the Study of Systems Science Vienna for public access.

About

The International Encyclopedia of Systems and Cybernetics was first edited and published by the system scientist Charles François in 1997. The online version that is provided here was based on the 2nd edition in 2004. It was uploaded and gifted to the center by ASC president Michael Lissack in 2019; the BCSSS purchased the rights for the re-publication of this volume in 200?. In 2018, the original editor expressed his wish to pass on the stewardship over the maintenance and further development of the encyclopedia to the Bertalanffy Center. In the future, the BCSSS seeks to further develop the encyclopedia by open collaboration within the systems sciences. Until the center has found and been able to implement an adequate technical solution for this, the static website is made accessible for the benefit of public scholarship and education.

A B C D E F G H I J K L M N O P Q R S T U V W Y Z

PERIOD-DOUBLING SEQUENCE 2)

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A succession of period-doubling bifurcations.

Period-doubling was discovered by M. FEIGENBAUM.

An orbit on the trajectory is replaced by another one twice as long at each time-step t, while the time needed for a repetition of any cycle is twice the number of time-steps. The longer the period, the faster the period doubling and the smaller the distance between neighbouring points on the orbit: This is a fractalization process.

In this way the process acquires a growingly random aspect that makes it more and more difficult to observe. A sequence of regular oscillations suddenly gives way to unpredictable behavior, and back again to a new pattern of oscillations, and so on, but within shorter and shorter time spans. The process remains however basically deterministic, at least globally.

A period-doubling sequence is the signature of chaos.

→ "Logistic equation"; "Renormalization". For more precise information, see JENSEN (1987).

Categories

  • 1) General information
  • 2) Methodology or model
  • 3) Epistemology, ontology and semantics
  • 4) Human sciences
  • 5) Discipline oriented

Publisher

Bertalanffy Center for the Study of Systems Science(2020).

To cite this page, please use the following information:

Bertalanffy Center for the Study of Systems Science (2020). Title of the entry. In Charles François (Ed.), International Encyclopedia of Systems and Cybernetics (2). Retrieved from www.systemspedia.org/[full/url]

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