Overview
- Deals with three types of the simplest dynamic systems: systems related to Gaussian random fields, to stochastic parametric excitation, and to stochastic parametric excitation fed by Gaussian pumping
- Presents the fundamentals of stochastic dynamic systems and natural science
- Written by a respected expert in the field
- Includes supplementary material: sn.pub/extras
Part of the book series: Understanding Complex Systems (UCS)
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Table of contents (10 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This book addresses the processes of stochastic structure formation in two-dimensional geophysical fluid dynamics based on statistical analysis of Gaussian random fields, as well as stochastic structure formation in dynamic systems with parametric excitation of positive random fields f(r,t) described by partial differential equations. Further, the book considers two examples of stochastic structure formation in dynamic systems with parametric excitation in the presence of Gaussian pumping. In dynamic systems with parametric excitation in space and time, this type of structure formation either happens – or doesn’t! However, if it occurs in space, then this almost always happens (exponentially quickly) in individual realizations with a unit probability.
In the case considered, clustering of the field f(r,t) of any nature is a general feature of dynamic fields, and one may claim that structure formation is the Law of Nature for arbitrary random fields of such type. The study clarifies the conditions under which such structure formation takes place. To make the content more accessible, these conditions are described at a comparatively elementary mathematical level by employing ideas from statistical topography.
Authors and Affiliations
Bibliographic Information
Book Title: Fundamentals of Stochastic Nature Sciences
Authors: Valery I. Klyatskin
Series Title: Understanding Complex Systems
DOI: https://doi.org/10.1007/978-3-319-56922-2
Publisher: Springer Cham
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-56921-5Published: 05 May 2017
Softcover ISBN: 978-3-319-86036-7Published: 09 May 2018
eBook ISBN: 978-3-319-56922-2Published: 28 April 2017
Series ISSN: 1860-0832
Series E-ISSN: 1860-0840
Edition Number: 1
Number of Pages: XII, 190
Number of Illustrations: 51 b/w illustrations, 11 illustrations in colour
Topics: Complexity, Complex Systems, Geotechnical Engineering & Applied Earth Sciences