 # 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.

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.

## MODELS (Mathematical) of systems2)

A. RAPOPORT discussed the possibilities for creating adequate mathematical models for real systems (1965), in the following terms: "G.S. theory… is primarily concerned with the structures of systems as defined by the relations which the parts of a system have to each other, in the way these relations determine the dynamic behavior of the system (its passage from state to state), and with the history of the system, i.e., its own development as a result of the interactions with its environment.

"A mathematical general systems theory provides descriptions of these three aspects of systems, namely structure, behavior and evolution, in abstract mathematical language. A typology of systems, accordingly, becomes a mathematical typology. Two systems are identical if the mathematical structures of their respective models are identical (or isomorphic to use the mathematical expression)" (1966, p.9).

It had possibly been better to say that two systems may have more or less similar mathematical models because their structures are isomorphic. Of course, RAPOPORT appreciates this point, as he writes, immediately: "The degree of similarity between the systems is estimated by the degree in which their mathematical models are related" (Ibid).

A unified and synthetic mathematical G.S. theory does not seem to exist. What we have are a number of mathematical theories related to some specifice structural or functional aspects of systems.

Even now, mathematical models for complex systems remain a tall order: very much remains to be done.

### 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). 