International Encyclopedia of Systems and Cybernetics

The French author B. WALLISER (1977 – hereafter W) and the Catalan systemist P. VOLTES BOU (1978 – hereafter VB) established different, but more or less complementary taxonomies of models. They have been completed by this compiler (Hereafter F) and coordinated as follows (alphabetic order used):

- Analogic: A model obtained by substitution of a set of interrelated properties by another, homomorphic of the former. (VB)

"A typical example are hydraulic artefacts used to represent economical or traffic systems" (VB).

- Closed: A model that only includes elements, relations and/or variables corresponding to endogenous states of a system (W).

- Digital: A computer model constructed according to a binary language (F).

- Disaggregative: A model that can be subdivided into sub models relatively independent from each others (W).

- Dynamic transferencial: A linear stationary and continuous model connecting in vectorial fashion inputs and outputs (W).

These models can lead to problems when one of the conditions limitative to dynamic stability is not anymore valid.

- Formal: A model established in a logical or mathematical abstract language (F).

- Global: A model aimed at describing the system as a set as complete as posssible.(W).

Systems dynamics models aim at globality.

Not for being "global" is the model a complete description of the system. It is necessarily obtained by aggregation, which implies simplifications. The way this is done reflects the conscious or unconscious decisions taken by the modeler.

Unfortunately, when the results are assessed, they are seldom put into perspective.

As observed with the "Club of Rome" models, they become easily controversial.

- Hierarchic: A model organized along various levels of complexity (F).

When static, they are called "organigrams" (in French and Spanish) and supposed to represent an organization in the form of a pyramid. When dynamic, they emphasize regulations and controls. (Flow charts)

- Iconic: A model in which the relevant elements and properties are represented in a figurative manner at some specified scale (VB).

Examples are photographies, drawings, maps, scale models, BOHR's "planetary" atom, stellar system models, etc… (VB).

- Interdependent: A model that may only be fragmented into closely interrelated submodels, representing very strongly interconnected subsystems (W).

- Macroscopic: A model including only interrelations among variables at the global level of the system (W).

- Metamodel: A model of a higher level of abstraction which maps the properties of lower systems models into propositions of a higher level of abstraction (J.P.van GIGCH, after St. BEER, – 1986, p.3).

van GIGCH states "Of necessity, the metamodel is conceptualised in a metasystemic language or meta logic which can decide propositions and reconcile arguments which cannot be decided or reconciled in the language or logic of lower systems models" (Ibid).

- Microscopic: A model including only interrelations among variables at the subsystems levels of the system (W).

- Open: A model that also includes exogenous variables, corresponding to inputs from the metasystem or environment and outputs into the same (W).

- Partial: A model describing merely a fragment of a subset of phenomena in the system (W).

- Physical: A physical representation of the system in form of concrete processes (W).

Good examples are reduced models of aircrafts for aerodynamic tests; reduced models of harbours or river basins for the study of currents, silting processes, etc…

- Recursive: A model that can be fragmented into succesive models offering the same intrinsic characteristics (W).

- Sequential: A model usable to study processes chaining in time (W).

In practice, it is quite difficult to create very reliable sequential models (i.e. useful for forecasting purposes), specially in complex systems which may present chaotic behavior. Most sequential models study the variations of only one process, assuming that all other conditions will remain constant.

- Short, mean or long term: Models that emphasize different time spans in the systems behavior (F).

While it is practically difficult to do, ideally short mean and long term models should be interconnected, even if this may lead to very complicated periodic or chaotic dynamics.

- Simultaneous: A model that represent the whole structure of a system at a given moment (W).

Such models could also be called "structural ", or "synchronic". They are instantaneous and static, and thus unfit to trace any process. It should never be forgotten that these models practically suppress the time dimension and tend sometimes to generate the illusion of total stability.

- Symbolic: A model that uses letters, numbers and other symbols to represent variables and their interrelations (VB).

In this sense, "symbolic' is practically equivalent to "formal"

Obviously, a model may include various of the characteristics previously described… Moreover, even WALLISER's and VOLTES BOU's listing remains partial (see former entries).

Other authors proposed different taxonomies of models, some of them more or less complementary, and some others offering finer subdivisions.

A. ROSENBLUETH and N. WIENER (1945) proposed two fundamental classes:

- Material models, i.e. simplified material representations of some of the characteristics of the original system;

- Formal models, i.e. mathematical simplified representations of structural or dynamic properties of the system.

D. and G.A. MIRHAM proposed an expanded classification as follows:

"Physical models

Replicas: Biological twins; earthen relief maps

Quasi-replicas: Silhouettes; planetarium shows

Analogue: White noise generators, statues

"Symbolic models

Descriptions: Textbook; metaphorical essay

Simulations: Operational, procedural description

Formalizations: Differential equation: Poisson distribution

"Hybrid models

Analogue-similar: Hybrid computer model of river flow and storage

Replica-descriptive: War gaming exercise

Replica-similar: Operational, computerized, gaming model

Others: Board games, such as Monopoly" (1975, p.43).

So many classes are somewhat baffling, but reflect the considerable complexity in the field of model building.