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 BIFURCATION 2)

A threshold in a process that tends to turn chaotic, signaled by the replacement of a period n cycle by a period 2n cycle.

After such a bifurcation the repetition of a certain state of the system needs twice the number of time-steps. When repeated time and again these events are akin to a fractalization of the cycles.

In the case of the logistic equation, as stated by R. JENSEN: "The range of (the parameter) a over which a single cycle is stable decreases rapidly as the period of the cycle increases, which accounts for the rapid accumulation of cycles with larger and larger periods" (1987, p.171).

For a ≥ 3,57 the global cycle's period becomes infinite.

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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