Wiederkehrzyklus

Wiederkehrzyklus, literally “recurrence cycle” in German, is a concept used to describe the time interval between successive occurrences of a defined state, event, or pattern within a system. It is applied across disciplines such as physics, engineering, geology, climatology, epidemiology, and reliability analysis. The term covers both deterministic cycles with a fixed period and stochastic recurrence times where events occur at irregular intervals.

In deterministic contexts, the Wiederkehrzyklus equals the fundamental period of the system, for example the time it takes for a perfectly periodic signal to repeat. In stochastic settings, recurrence times are random variables with a probability distribution. Renewal theory studies these inter-arrival times, and the mean recurrence time is related to the event rate. For a homogeneous Poisson process, the recurrence time is exponentially distributed with mean 1/λ; more complex processes may exhibit time-varying or memory effects.

Geoscience and environmental disciplines frequently use the concept as a recurrence interval or return period for extreme events, such as floods or earthquakes, derived from historical records and statistical modeling. These estimates inform risk assessment, infrastructure design, insurance, and land-use planning, though they depend on data quality and assumptions of stationarity.

Estimating a Wiederkehrzyklus involves analyzing time series of events, fitting inter-event-time distributions, and assessing uncertainty. Limitations include non-stationarity, limited data for rare events, and the challenge of defining what constitutes a comparable recurrence.

Related concepts include period, cycle, recurrence plot, and renewal theory.