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

SYSTEM (Nonlinear) 2)

← Back

Any system with various simultaneously interacting causal lines that impede rigorous globally deterministic behavior.

L. DOUGLAS KIEL writes: "Linear systems respond to minimal changes in their parameters, or to external shocks, in a smooth and proportionate manner" (1992, p.30).

It is really very difficult to conceive a system which would be truly linear. Models of systems are frequently linear, indeed. But their reliability is generally limited to a small and short term range of the system's behavior.

DOUGLAS KIEL writes: "A small change in a nonlinear system can, however, produce an enormous difference in the structure and behavior of the system" (Ibid).

However, many small changes have no such effects, with the result that we may well believe in a non-existant long term dynamic (or even static!) stability.

"…external disturbances may amplify nonlinear interactions, generating instabilities, that may initiate a break with the pre-existing behavioral and structural regimes" (Ibid).

"Nonlinear systems may also reveal a "sensitive dependence on initial conditions" (J. GLEICK, 1987).

"A small difference in the initial conditions of seemingly similar nonlinear systems can lead to dramatically different evolutionary paths and outcomes….Any effort at forecasting the behavior of a nonlinear system is, thus a highly suspect activity" (Ibid).

This is possibly somewhat over-pessimistic: With good monitoring, a sufficient grasp of chaos theory, and as much as possible consolidated knowledge of the various levels of cyclical activity of the system, some forecasting is feasible… but the results should always be taken with caution.

According to DOUGLAS KIEL: "Nonlinear systems exhibit four distinct types of temporal behavior…

1) convergence to a stability or equilibrium

2) stable oscillation

3) unstable and explosive

4) chaotic.

Each regime can appear within the long term behavior of a nonlinear system" (Ibid).

Another important aspect is, in P.M. ALLEN et al. words: "…nonlinear systems, operating far from thermodynamic equilibrium, can undergo successive structural instabilities leading to a progressive complexification of their organization and functioning. Such phenomena involve a dialogue between stochastic and deterministic aspects of the system, as the interaction tend to a "self-organization" process of successive periods of stability and instability, where new qualities, traits and characteristic emerge over time" (1984, p.150).

Evolution seems thus to offer a "punctuated" character, as claimed in living systems by GOULD and ELDREDGE.

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