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Analysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems - Using the Methods of Stochastic Processes (Paperback, 1st ed. 2019)
Loot Price: R3,367
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Analysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems - Using the Methods of Stochastic Processes (Paperback, 1st ed. 2019)
Series: Understanding Complex Systems
Expected to ship within 10 - 15 working days
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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.
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