## PERIODICITY
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The more ore less regularly recurrent and more or less similar variations of a function or a systems behavior.

Periodicity implies a succession of cycles of regular or irregular frequencies and amplitudes. The following types of periodicities could be distinguished:

- mono-cyclical: corresponding to only one cycle of defined frequency and amplitude. Such periodicity is perfectly predictable. In many cases, when others cycles with very short or very long frequencies and amplitude are present, they escape observation for long time, or they seem to be trends and the mono-cyclical model remains generally adequate.

- commensurable, bi- or poly-cyclical: this case corresponds to the interferences and combinations of cycles of various commensurable frequencies in harmonic relation in phase or out of phase (f.ex. 2, 3. and 6 or, more complicated, 9, 12, 27). Such periodicities are still regular and predictable, but more intricated, difficult to observe and complicated to analyse. In some cases, fractal periodicities can be found. See: "Self-similarity in WEIERSTRASS functions".

- uncommensurable: This case corresponds to the interferences of various cycles with frequencies corresponding to prime numbers. In simple cases (f. ex. 2, 3, 5, and 7), observation and predictability seems still more or less manageable, using lowest common multiples (here, 210). However, for compositions of more, or greater prime numbers, regularities may become practically unobservable and the system may appear chaotic, i.e. globally deterministic only in the very long term and this merely in case of absence of any environmental perturbation.

### 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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