## MODELS (Mathematical) of systems
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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).

→ ("G.S.T.: Mathematical aspects").

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.

→ (G.S.T.: Mathematical aspects, and herafter).

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).

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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