I am a student currently doing a course on modelling and simulation. I came across the classifications of mathematical models and studied that they can classified as static or dynamic, deterministic or stochastic, and as discrete or continuous. This means any mathematical model may belong to one of the 8 categories as shown in the picture below.

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Although I am able to understand every classification, I am unable to find real world examples for each type of model. Can someone give good examples for each of the 8 classifications shown here?

  • $\begingroup$ You should post the examples that you have come up with. $\endgroup$
    – A.E
    Jul 2, 2013 at 1:20
  • $\begingroup$ I don't think the tag "model categories" belongs to this post, since it should refer to a branch of category theory... $\endgroup$ Jul 2, 2013 at 17:22
  • $\begingroup$ This is a classification in terms of tools used, which is not as relevant to scientists as a classification based on intent of the model. $\endgroup$ Dec 17, 2013 at 16:39

2 Answers 2


Deterministic-Static-Discrete: Clock cycles for a computer program to run on a given input.

Deterministic-Static-Continuous: Amount of fluid a pipe can hold before breaking.

Deterministic-Dynamic-Discrete: CPU percentage upon startup

Deterministic-Dynamic-Continuous: Arguably everything part of the classical physical model

Stochastic-Static-Discrete: Dice roll outcomes

Stochastic-Static-Continuous: Distance from bullseye on a dart throw (could be considered continuous, especially if the quantity is being compared by competing players)

Stochastic-Dynamic-Discrete: Gambler's Running Total

Stochastic-Dynamic-Continuous: Weather


I'm concerned that not all mathematical models are time based. For example you might want to model the frequency domain response of a filter specified in the S-Domain. This is a Deterministic-Static-Continuous model, but neither static nor continuous in time. It's static and continuous in the frequency domain (because the equations are analytic).

I believe this is a good octo-chart for dynamical models.


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