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

GROWTH-RATE PARAMETER 2)

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The factor which controls growth rate.

Since no growth process is independent of its environmental conditions and/or intrinsic characteristics, none can be linear at long-term. This must be reflected into growth equations if real situations are to be satisfactorily modelled.

Thus a growth-rate parameter must be introduced into the equation.

According to J. GLEICK: "In the physical systems from which these equations were borrowed, that parameter corresponded to the amount of heating, or the amount of friction, or the amount of some other "messy" quantity. In short, the amount of nonlinearity" (1987, p.63).

R. JENSEN uses as an example a very simple difference equation:

Xn+1 = axn (1-xn) or Xn+1 = aXn – axn

He writes: "The time-evolution of xn generated by this single algebraic equation exhibits an extraordinary transformation from order to chaos as the parameter a, which measures the strength of nonlinearity is increased" (1987, p.170).

For x included between 0 and 1 and for different values of a, JENSEN distinguishes the following cases:

- for a = 1 – Growth followed by monotonic damping and extinction;

- for a = 2,9 Growth toward an asymptotic stability with a punctual attractor (variable according to the value of a);

- for a = 3,2 Growth followed by fluctuations around a stable cycle limit;

- for a = 4,0 Growth followed by apparently random fluctuations (chaos).

For a clearer understanding, see reference.

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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