Analysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems : Using the Methods of Stochastic Processes / by M. Reza Rahimi Tabar.

Format:

Book

Author/Creator:

Rahimi Tabar, M. Reza, author.

Contributor:

SpringerLink (Online service)

Series:

Physics and Astronomy (Springer-11651)

Understanding complex systems 1860-0832

Understanding Complex Systems, 1860-0832

Language:

English

Subjects (All):

Statistical physics.

Dynamics.

System theory.

Probabilities.

Economics.

Computational complexity.

Neurosciences.

Complex Systems.

Probability Theory and Stochastic Processes.

Economic Theory/Quantitative Economics/Mathematical Methods.

Complexity.

Local Subjects:

Complex Systems.

Probability Theory and Stochastic Processes.

Economic Theory/Quantitative Economics/Mathematical Methods.

Complexity.

Neurosciences.

Physical Description:

1 online resource (XVIII, 280 pages) : 41 illustrations, 22 illustrations in color.

Edition:

First edition 2019.

Contained In:

Springer eBooks

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2019.

System Details:

text file PDF

Summary:

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.

Contents:

1 Introduction

2 Introduction to Stochastic Processes

3 Kramers-Moyal Expansion and Fokker-Planck Equation

4 Continuous Stochastic Process

5 The Langevin Equation and Wiener Process

6 Stochastic Integration, It^o and Stratonovich Calculi

7 Equivalence of Langevin and Fokker-Planck Equations

8 Examples of Stochastic Calculus

9 Langevin Dynamics in Higher Dimensions

10 Levy Noise Driven Langevin Equation and its Time Series-Based Reconstruction

11 Stochastic Processes with Jumps and Non-Vanishing Higher-Order Kramers-Moyal Coefficients

12 Jump-Diffusion Processes

13 Two-Dimensional (Bivariate) Jump-Diffusion Processes

14 Numerical Solution of Stochastic Differential Equations: Diffusion and Jump-Diffusion Processes

15 The Friedrich-Peinke Approach to Reconstruction of Dynamical Equation for Time Series: Complexity in View of Stochastic Processes

16 How To Set Up Stochastic Equations For Real-World Processes: Markov-Einstein Time Scale

17 Reconstruction of Stochastic Dynamical Equations: Exemplary Stationary Diffusion and Jump-Diffusion Processes

18 The Kramers-Moyal Coefficients of Non-Stationary Time series in The Presence of Microstructure (Measurement) Noise

19 Influence of Finite Time Step in Estimating of the Kramers-Moyal Coefficients

20 Distinguishing Diffusive and Jumpy Behaviors in Real-World Time Series

21 Reconstruction of Langevin and Jump-Diffusion Dynamics From Empirical Uni- and Bivariate Time Series

22 Applications and Outlook

23 Epileptic Brain Dynamics.

Other Format:

Printed edition:

ISBN:

978-3-030-18472-8

9783030184728

Access Restriction:

Restricted for use by site license.