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

ATTRACTORS; A classification 1)2)

K.De GREENE proposes the following classification of attractors:

"1. Points, like the static equilibrium points of catastrophe theory. Points can apply to both linear and non-linear systems.

"2. Periodic attractors, like limit cycles that apply, say, to interacting populations

"3. Strange, Lorenz or chaotic attractors: A system state can be related to a basin of attraction, but how stable the system is and where the system resides relative to the boundary of the basin may be unknown and unknowable. Indeed, the very existence of an alternative basin(s) of attraction may be unknown".(1990, p.161)

Furthermore "…minuscule differences in initial conditions may lead to the exponential expansion of these differences" (Ibid.)

A slightly different classification is possible: Fixed point: The simplest attractor. It corresponds to a generally monotonous trajectory of a non disturbed system toward a final state, for example: a real pendulum, submitted to frictions.

("Fixed point")

Limit cycle: Corresponds to a closed loop within the phases space. This implies that the system's trajectory involves a series of nondisturbed periodic oscillations.

Toric attractor: Characterizes the behavior of a system simultaneously submitted to two periodic oscillations, independent from each other. The structure of these oscillations remains always predictable and possible to carry out, even when the periods are incommensurable.

"Numbers (Prime)"

Chaotic attractor: Corresponds to the behavior of a system simultaneously submitted to, at least, three periodic oscillations independent from each others. The simplest corresponds to systems of simple differential equations where the phases space is three-dimensional.

Even in these cases the transformations of the system are generally not predictable. An early example was the famous astronomical three bodies problem studied by POINCARÉ.

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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