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.

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LIMIT CYCLE (Stable) (= Attractor) 2)

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"Closed integral curve which represents a periodic regime" (M. DUBOIS et al, 1987, p.193).

This representation, introduced by H. POINCARÉ, was indeed the first example of a (non punctual) attractor.

In order to obtain it, POINCARÉ introduced the notion of transverse arc: it is an arc of curve, which is tangent to none of the points of an integral curve (meaning that it intersects many times with the latter). Considering the succession of the intersections of an integral curve with a transverse arc, he reduces the study of the curve in the plane to the study of the succession of points on a line. POINCARÉ next shows that any integral curve which does not end into a singular point is a cycle or a spiral asymptotically winding around the cycle, which he thus calls a limit cycle." (J.L. CHABERT & A. DAHAN DALMEDICO, 1991, p.568).

The limit cycle corresponds to the VAN DER POL equation which "describes the behavior of an oscillator which is kept going, with increase of the oscillations of reduced amplitude and decrease of those of wide amplitude." (P. BERGE et al, 1984, p.26).

Any trajectory of this kind converges towards the limit cycle, which corresponds to the type of systems tending to oscillating dynamic stability.

The basic condition for the existence of a limit cycle is a constant input of sufficient energy to the system. However, an excess of energy may throw it out of its stability range, in accordance with thermodynamics of systems far-from-equilibrium.

→ Cycle (Limit); Cycle (Stable limit)

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  • 1) General information
  • 2) Methodology or model
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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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