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Understanding Complex Systems

Analysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems

Using the Methods of Stochastic Processes

Authors: Rahimi Tabar, M. Reza

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  • Presents an advanced and systematic approach for analyzing the stationary or non-stationary time series
  • Provides an inverse method on how to construct stochastic evolution equation from given time series
  • Offers a non-parametric approach: all functions and parameters of the constructed stochastic evolution equation are determined directly from the measured time series
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eBook 107,09 €
price for Spain (gross)
  • ISBN 978-3-030-18472-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 135,19 €
price for Spain (gross)
  • ISBN 978-3-030-18471-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this book

This book focuses on a central question in the field of complex systems: Given a fluctuating (in time or space), uni- or multi-variant sequentially measured set of experimental data (even noisy data), how should one analyse non-parametrically the data, assess underlying trends, uncover characteristics of the fluctuations (including diffusion and jump contributions), and construct a stochastic evolution equation?

Here, the term "non-parametrically" exemplifies that all the functions and parameters of the constructed stochastic evolution equation can be determined directly from the measured data.

The book provides an overview of methods that have been developed for the analysis of fluctuating time series and of spatially disordered structures.  Thanks to its feasibility and simplicity, it has been successfully applied to fluctuating time series and spatially disordered structures of complex systems studied in scientific fields such as physics, astrophysics, meteorology, earth science, engineering, finance, medicine and the neurosciences, and has led to a number of important results.

The book also includes the numerical and analytical approaches to the analyses of complex time series that are most common in the physical and natural sciences. Further, it is self-contained and readily accessible to students, scientists, and researchers who are familiar with traditional methods of mathematics, such as ordinary, and partial differential equations.

The codes for analysing continuous time series are available in an R package developed by the research group Turbulence, Wind energy and Stochastic (TWiSt) at the Carl von Ossietzky University of Oldenburg under the supervision of Prof. Dr. Joachim Peinke. This package makes it possible to extract the (stochastic) evolution equation underlying a set of data or measurements.

About the authors

Mohammad Reza Rahimi Tabar is Professor in Physics Department of Sharif University of Technology and published over 120 articles in scientific journals. He was fellow of the Alexander von Humboldt Foundation at Oldenburg and Bonn Universities, Mercator guest professor at Osnabrück University and associate member of ICTP - International Centre for Theoretical Physics.


Table of contents (24 chapters)

Table of contents (24 chapters)

Buy this book

eBook 107,09 €
price for Spain (gross)
  • ISBN 978-3-030-18472-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 135,19 €
price for Spain (gross)
  • ISBN 978-3-030-18471-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Analysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems
Book Subtitle
Using the Methods of Stochastic Processes
Authors
Series Title
Understanding Complex Systems
Copyright
2019
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-18472-8
DOI
10.1007/978-3-030-18472-8
Hardcover ISBN
978-3-030-18471-1
Series ISSN
1860-0832
Edition Number
1
Number of Pages
XVIII, 280
Number of Illustrations
19 b/w illustrations, 22 illustrations in colour
Topics