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  • © 2019

Analysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems

Using the Methods of Stochastic Processes

  • 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

Part of the book series: Understanding Complex Systems (UCS)

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eBook USD 109.00
Price excludes VAT (USA)
  • ISBN: 978-3-030-18472-8
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 139.99
Price excludes VAT (USA)
Hardcover Book USD 179.99
Price excludes VAT (USA)

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Table of contents (24 chapters)

  1. Front Matter

    Pages i-xviii
  2. Introduction

    • M. Reza Rahimi Tabar
    Pages 1-8
  3. Introduction to Stochastic Processes

    • M. Reza Rahimi Tabar
    Pages 9-18
  4. Continuous Stochastic Processes

    • M. Reza Rahimi Tabar
    Pages 31-37
  5. The Langevin Equation and Wiener Process

    • M. Reza Rahimi Tabar
    Pages 39-48
  6. Example of Stochastic Calculus

    • M. Reza Rahimi Tabar
    Pages 69-78
  7. Langevin Dynamics in Higher Dimensions

    • M. Reza Rahimi Tabar
    Pages 79-86
  8. Jump-Diffusion Processes

    • M. Reza Rahimi Tabar
    Pages 111-121
  9. Two-Dimensional (Bivariate) Jump-Diffusion Processes

    • M. Reza Rahimi Tabar
    Pages 123-128

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.

Keywords

  • Time Series Analysis
  • Langevin Dynamics
  • Jump-Diffusion Dynamics
  • From Time Series to Dynamical Equation
  • Modeling epileptic Brain Dynamics
  • Dynamics of Optically Trapped Particles
  • Jumpy Stochastic Behavior
  • Diffusive Stochastic Behavior
  • Jump-Diffusion Processes
  • Discontinuous Stochastic Processes
  • Modeling complex dynamical systems
  • Physics of stochastic processes
  • complexity

Authors and Affiliations

  • Department of Physics, Sharif University of Technology, Tehran, Iran

    M. Reza Rahimi Tabar

About the author

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.


Bibliographic Information

Buying options

eBook USD 109.00
Price excludes VAT (USA)
  • ISBN: 978-3-030-18472-8
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 139.99
Price excludes VAT (USA)
Hardcover Book USD 179.99
Price excludes VAT (USA)