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Stochastic dynamical systems - Scholarpedia

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A stochastic dynamical system is a dynamical system subjected to the effects of noise. Such effects of fluctuations have been of interest for over a century since the seminal work of Einstein (1905). Fluctuations are classically referred to as "noisy" or "stochastic" when their suspected origin implicates the action of a very large number of variables or "degrees of freedom". For example, the action of many water molecules on the motion of a large protein can be seen as noise. In principle the equations of motion for such high-dimensional dynamics can be written and studied analytically and numerically. However, it is possible to study a system subjected to the action of the large number of variables by coupling its deterministic equations of motion to a "noise" that simple mimics the perpetual action of many variables. The coupling of noise to nonlinear deterministic equations of motion can lead to non-trivial effects (Schimansky-Geier 1985; Horsthemke 1985; Haenggi, Talkner and Borko

A stochastic dynamical system is a dynamical system subjected to the effects of noise. Such effects of fluctuations have been of interest for over a century since the seminal work of Einstein (1905). Fluctuations are classically referred to as "noisy" or "stochastic" when their suspected origin implicates the action of a very large number of variables or "degrees of freedom". For example, the action of many water molecules on the motion of a large protein can be seen as noise. In principle the equations of motion for such high-dimensional dynamics can be written and studied analytically and…

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