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

MATHEMATICS and nonlinear systems 1)2)3)

← Back

According to R. MAY: "The elegant body of mathematical theory pertaining to linear systems (Fourier analysis, orthogonal functions, and so on) and its sucessful application to many fundamentally linear problems in the physical sciences, tends to dominate even moderately advanced University courses in mathematics and theoretical physics. The mathematical intuition so developed ill equips the student to confront the bizarre behavior exhibited by the simplest of discrete nonlinear systems… Yet, such nonlinear systems are surely the rule, not the exception, outside the physical sciences" (1976, p.467).

The trend to use linear mathematics in social sciences, for instance, has been a stumbling block for the use of systems concepts by sociologists and explains some of their sharp criticism. In J. MARTINO's words in his review of BERLINSKI's "On Systems Analysis": "There is no proof offered by the systems analysts that social and political systems are at all similar to control systems" (1979, p.18).

MAY advocates the study of 1st order nonlinear difference equations, as a starting point. Since 1976, when he published this paper, a considerable body of new mathematics of nonlinearity has been created.

It should be emphasized however that the first important work on nonlinearity was POINCARÉ's 1889 paper on the three bodies problem and that POINCARÉ himself introduced various topological concepts that led to chaos theory.

→ Poincaré Section

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