The Fokker-Planck Equation Methods of Solution and Applications
This book deals with the derivation of the Fokker-Planck equation, methods of solving it and some of its applications. Various methods such as the simulation method, the eigenfunction expansion, numerical integration, the variational method, and the matri
- PDF / 34,504,560 Bytes
- 486 Pages / 482 x 686 pts Page_size
- 25 Downloads / 175 Views
Springer Berlin Heidelberg New York Barcelona Budapest Hong Kong London Milan Paris Singapore Tokyo
Springer Series in Synergetics
Editor: Hermann Haken
An ever increasing number of scientific disciplines deal with complex systems. These are systems that are composed of many parts which interact with one another in a more or less complicated manner. One of the most striking features of many such systems is their ability to spontaneously form spatial or temporal structures. A great variety of these structures are found, in both the inanimate and the living world. In the inanimate world of physics and chemistry, examples include the growth of crystals, coherent oscillations oflaser light, and the spiral structures formed in fluids and chemical reactions. In biology we encounter the growth of plants and animals (morphogenesis) and the evolution of species. In medicine we observe, for instance, the electromagnetic activity of the brain with its pronounced spatio-temporal structures. Psychology deals with characteristic features of human behavior ranging from simple pattern recognition tasks to complex patterns of social behavior. Examples from sociology include the formation of public opinion and cooperation or competition between social groups. In recent decades, it has become increasingly evident that all these seemingly quite different kinds of structure formation have a number of important features in common. The task of studying analogies as well as differences between structure formation in these different fields has proved to be an ambitious but highly rewarding endeavor. The Springer Series in Synergetics provides a forum for interdisciplinary research and discussions on this fascinating new scientific challenge. It deals with both experimental and theoretical aspects. The scientific community and the interested layman are becoming ever more conscious ofconcepts such as self-organization, instabilities, deterministic chaos, nonlinearity, dynamical systems, stochastic processes, and complexity. All of these concepts are facets of a field that tackles complex systems, namely synergetics. Students, research workers, university teachers, and interested laymen can find the details and latest developments in the Springer Series in Synergetics, which publishes textbooks, monographs and, occasionally, proceedings. As witnessed by the previously published volumes, this series has always been at the forefront of modern research in the above mentioned fields. It includes textbooks on all aspects of this rapidly growing field, books which provide a sound basis for the study of complex systems. A selection of volumes in the Springer Series in Synergetics:
8 13 15
18 19 20 21 24 32
Synergetics An Introduction 3rd Edition By H. Haken Stochastic Nonlinear Systems Editors: L. Arnold, R. Lefever Handbook of Stochastic Methods 2nd Edition By C. W. Gardiner Noise-Induced Transitions Theory and Applications in Physics, Chemistry, and Biology By W. Horsthemke, R. Lefever The Fokker-Planck Equation 2nd Edition By H. Risken Che
