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Fokker-Planck equation --- Fokker-Planck, Equation de --- Fokker-Planck equation.

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Nature is inherently noisy and nonlinear. It is noisy in the sense that all macroscopic systems are subject to the fluctuations of their environments and also to internal fluctuations. It is nonlinear in the sense that the restoring force on a system displaced from equilibrium does not usually vary linearly with the size of the displacement. To calculate the properties of stochastic (noisy) nonlinear systems is in general extremely difficult, although considerable progress has been made in the past. The three volumes that make up Noise in Nonlinear Dynamical Systems comprise a collection of specially written authoritative reviews on all aspects of the subject, representative of all the major practitioners in the field. The first volume deals with the basic theory of stochastic nonlinear systems. It includes an historical overview of the origins of the field, chapters covering some developed theoretical techniques for the study of coloured noise, and the first English-language translation of the landmark 1933 paper by Pontriagin, Andronov and Vitt.

Fokker-Planck equation.

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Dynamische Systeme sind durch die Angabe des Zeitverlaufs ihrer Zustandsvariablen vollständig beschreibbar. Diese Form ist jedoch für eine mathematische Bearbeitung ungeeignet. Die Datenmenge reduziert sich um ein vielfaches und eine mathematische Behandlung wird ermöglicht, wenn zur Beschreibung der dynamischen Systeme charakteristische Größen herangezogen werden. In dieser Arbeit werden mit der phänomenologischen Herangehensweise durch eine Untersuchung der Verteilungsdichten die Bifurkationen in stochastischen dynamischen Systemen beschrieben.

Fokker-Planck equation.

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Statistical physics --- Fokker-Planck equation --- Fokker-Planck, Equation de

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This advanced undergraduate and graduate text has now been revised and updated to cover the basic principles and applications of various types of stochastic systems, with much on theory and applications not previously available in book form. The text is also useful as a reference source for pure and applied mathematicians, statisticians and probabilists, engineers in control and communications, and information scientists, physicists and economists.Has been revised and updated to cover the basic principles and applications of various types of stochastic systemsUseful as

Stochastic differential equations. --- Differential equations --- Fokker-Planck equation