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Each of these bifurcation points is a period-doubling bifurcation. The ratio of the lengths of successive intervals between values of r for which bifurcation occurs converges to the first Feigenbaum constant. The diagram also shows period doublings from 3 to 6 to 12 etc., from 5 to 10 to 20 etc., and so forth.
The return period then corresponds to the expected waiting time until the exceedance occurs again. The return period has the same dimension as the time for which each observation is representative. For example, when the observations concern daily rainfalls, the return period is expressed in days, and for yearly rainfalls it is in years.
A return period, also known as a recurrence interval or repeat interval, is an average time or an estimated average time between events such as earthquakes, floods, [1] landslides, [2] or river discharge flows to occur. It is a statistical measurement typically based on historic data over an extended period, and is used usually for risk analysis.
To get an IDF curves from a probability distribution, it is necessary to mathematically isolate the total amount or depth of the event , which is directly related to the average intensity and the duration , by the equation =, and since the return period is defined as the inverse of (), the function is found as the inverse of (), according to:
First order LTI systems are characterized by the differential equation + = where τ represents the exponential decay constant and V is a function of time t = (). The right-hand side is the forcing function f(t) describing an external driving function of time, which can be regarded as the system input, to which V(t) is the response, or system output.
In astrodynamics, an orbit equation defines the path of orbiting body around central body relative to , without specifying position as a function of time.Under standard assumptions, a body moving under the influence of a force, directed to a central body, with a magnitude inversely proportional to the square of the distance (such as gravity), has an orbit that is a conic section (i.e. circular ...
The anomalistic period is the time that elapses between two passages of an object at its periapsis (in the case of the planets in the Solar System, called the perihelion), the point of its closest approach to the attracting body. It differs from the sidereal period because the object's semi-major axis typically advances slowly.
In astronomy, a period-luminosity relation is a relationship linking the luminosity of pulsating variable stars with their pulsation period. The best-known relation is the direct proportionality law holding for Classical Cepheid variables , sometimes called the Leavitt Law .