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

FEIGENBAUM's NUMBER 2)5)

← Back

FEIGENBAUM's number is related to period-doubling sequences in systems turning chaotic through the increase of parameter a in the difference equation Xn+1 = aXn (1-xn), which can also be written in its quadratic form Xn+1 = aXn - aXn , where the second term is nonlinear.

R.V. JENSEN states: "As a is increased, the long-time motion converges to period – 8, – 16, – 32, – 64… cycles, finally accumulating to a cycle of infinite period for a = ainf ~3,57… FEIGENBAUM was able to prove, using a remarquable application of the renormalization group, that the intervals over which a cycle is stable decrease at a geometric rate of ~ 4,6692016. The tremendous significance of this work is that this rate and other properties of the period-doubling bifurcation sequence are universal in the sense that they appear in the dynamics of any system which can be approximately modeled by a nonlinear map with a quadratic extremum. FEIGENBAUM's theory has subsequently been confirmed in a wide variety of physical systems such as turbulent fluids, oscillating chemical reactions, nonlinear electric circuits, and ring lasers" (1987, p.171).

It would be very interesting to see if this property conducive to the onset of chaos is also present in ecological, economic and social systems.

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]

We thank the following partners for making the open access of this volume possible:

© 2020 BCSSS Contact/Imprint