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.

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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

INITIAL CONDITIONS (Sensibility to) 1)2)5)

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A condition in a nonlinear system by which very slight differences in initial conditions lead to considerable ones in the later behavior of the system.

More than one century ago, H. POINCARÉ, in his study "On the three bodies problem and the equations of dynamics" (1889). showed the impossibility to determine in an absolutely rigorous way the future positions of three (or N) interacting bodies: the problem cannot be satisfactorily integrated.

The basic cause of such a situation is that a 3-bodies (or more) system is not deterministic in a linear way.

N. PEGUIRON writes on this topic: "This sensibility to initial conditions, characteristic to any long term deterministic prediction, showed by POINCARE, is a general case in classical mechanics: only some quite simple cases escape to this, as for example the two-bodies system" (1989,p. 11).

In more complex cases, the discrepancies, not being still important, may remain unheeded during more or less a long time. This is what allows for example for apparently rigorous prediction of the astronomical trajectories. However, at long or very long term, it has been recently demonstrated that even the solar system is not absolutely stable.

PEGUIRON comments this situation in the following way: "Indeterminism in classical mechanics does not appears in their governing equations, but through the impossibility to apply them to a system not devoid of external influences. Clearly, in this case, the isolation process displays a property, (rigorous) determinism, which is not proper of real systems" (p.11).

The sensibility to initial conditions leads to chaotic behavior, i.e. to unpredictability, which grows with time. However this does not imply the total disappearance of global determinism.

POINCARÉ established the bases for the study of deterministic chaos, when he created the concepts of limit cycle, transverse arc and section normal to the trajectory, now called "POINCARÉ's section".

The non-instantaneous transmission of local causes and the non-simultaneity of the resulting effects makes up another way to account for partial and local breaches of determinism and of the unpredictable character of the trajectories bifurcations.

→ Sensibility to initial conditions

Categories

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

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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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