Analysis And Data Based Reconstruction Of Complex Nonlinear Dynamical Systems
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Analysis And Data Based Reconstruction Of Complex Nonlinear Dynamical Systems
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Author : M. Reza Rahimi Tabar
language : en
Publisher: Springer
Release Date : 2019-07-04
Analysis And Data Based Reconstruction Of Complex Nonlinear Dynamical Systems written by M. Reza Rahimi Tabar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-04 with Science categories.
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.
Nonlinear Dynamics In Physiology
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Author : Mark Shelhamer
language : en
Publisher: World Scientific
Release Date : 2007
Nonlinear Dynamics In Physiology written by Mark Shelhamer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Science categories.
This book provides a compilation of mathematical-computational tools that are used to analyze experimental data. The techniques presented are those that have been most widely and successfully applied to the analysis of physiological systems, and address issues such as randomness, determinism, dimension, and nonlinearity. In addition to bringing together the most useful methods, sufficient mathematical background is provided to enable non-specialists to understand and apply the computational techniques. Thus, the material will be useful to life-science investigators on several levels, from physiologists to bioengineer.Initial chapters present background material on dynamic systems, statistics, and linear system analysis. Each computational technique is demonstrated with examples drawn from physiology, and several chapters present case studies from oculomotor control, neuroscience, cardiology, psychology, and epidemiology. Throughout the text, historical notes give a sense of the development of the field and provide a perspective on how the techniques were developed and where they might lead. The overall approach is based largely on the analysis of trajectories in the state space, with emphasis on time-delay reconstruction of state-space trajectories. The goal of the book is to enable readers to apply these methods to their own research.
Nonlinear Dynamics And Statistics
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Author : Alistair I. Mees
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Dynamics And Statistics written by Alistair I. Mees and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Business & Economics categories.
All models are lies. "The Earth orbits the sun in an ellipse with the sun at one focus" is false, but accurate enough for almost all purposes. This book describes the current state of the art of telling useful lies about time-varying systems in the real world. Specifically, it is about trying to "understand" (that is, tell useful lies about) dynamical systems directly from observa tions, either because they are too complex to model in the conventional way or because they are simply ill-understood. B(:cause it overlaps with conventional time-series analysis, building mod els of nonlinear dynamical systems directly from data has been seen by some observers as a somewhat ill-informed attempt to reinvent time-series analysis. The truth is distinctly less trivial. It is surely impossible, except in a few special cases, to re-create Newton's astonishing feat of writing a short equation that is an excellent description of real-world phenomena. Real systems are connected to the rest of the world; they are noisy, non stationary, and have high-dimensional dynamics; even when the dynamics contains lower-dimensional attractors there is almost never a coordinate system available in which these at tractors have a conventionally simple description.
Nonlinear Dynamics And Chaos With Applications To Hydrodynamics And Hydrological Modelling
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Author : Slavco Velickov
language : en
Publisher: CRC Press
Release Date : 2014-04-21
Nonlinear Dynamics And Chaos With Applications To Hydrodynamics And Hydrological Modelling written by Slavco Velickov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-21 with Science categories.
The theory of nonlinear dynamics and chaos, and the extent to which recent improvements in the understanding of inherently nonlinear natural processes present challenges to the use of mathematical models in the analysis of water and environmental systems, are elaborated in this work.
The New Frontier Of Network Physiology From Temporal Dynamics To The Synchronization And Principles Of Integration In Networks Of Physiological Systems
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Author : Plamen Ch. Ivanov
language : en
Publisher: Frontiers Media SA
Release Date : 2022-02-17
The New Frontier Of Network Physiology From Temporal Dynamics To The Synchronization And Principles Of Integration In Networks Of Physiological Systems written by Plamen Ch. Ivanov and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-17 with Science categories.
Tms 2023 152nd Annual Meeting Exhibition Supplemental Proceedings
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Author : The Minerals, Metals & Materials Society
language : en
Publisher: Springer Nature
Release Date : 2023-02-06
Tms 2023 152nd Annual Meeting Exhibition Supplemental Proceedings written by The Minerals, Metals & Materials Society and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-06 with Technology & Engineering categories.
This collection presents papers from the 152nd Annual Meeting & Exhibition of The Minerals, Metals & Materials Society.
Topics In Nonlinear Time Series Analysis With Implications For Eeg Analysis
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Author : Andreas Galka
language : en
Publisher: World Scientific
Release Date : 2000-02-18
Topics In Nonlinear Time Series Analysis With Implications For Eeg Analysis written by Andreas Galka and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-02-18 with Science categories.
This book provides a thorough review of a class of powerful algorithms for the numerical analysis of complex time series data which were obtained from dynamical systems. These algorithms are based on the concept of state space representations of the underlying dynamics, as introduced by nonlinear dynamics. In particular, current algorithms for state space reconstruction, correlation dimension estimation, testing for determinism and surrogate data testing are presented — algorithms which have been playing a central role in the investigation of deterministic chaos and related phenomena since 1980. Special emphasis is given to the much-disputed issue whether these algorithms can be successfully employed for the analysis of the human electroencephalogram.
Dynamic Mode Decomposition
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Author : J. Nathan Kutz
language : en
Publisher: SIAM
Release Date : 2016-11-23
Dynamic Mode Decomposition written by J. Nathan Kutz and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-23 with Science categories.
Data-driven dynamical systems is a burgeoning field?it connects how measurements of nonlinear dynamical systems and/or complex systems can be used with well-established methods in dynamical systems theory. This is a critically important new direction because the governing equations of many problems under consideration by practitioners in various scientific fields are not typically known. Thus, using data alone to help derive, in an optimal sense, the best dynamical system representation of a given application allows for important new insights. The recently developed dynamic mode decomposition (DMD) is an innovative tool for integrating data with dynamical systems theory. The DMD has deep connections with traditional dynamical systems theory and many recent innovations in compressed sensing and machine learning. Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems, the first book to address the DMD algorithm, presents a pedagogical and comprehensive approach to all aspects of DMD currently developed or under development; blends theoretical development, example codes, and applications to showcase the theory and its many innovations and uses; highlights the numerous innovations around the DMD algorithm and demonstrates its efficacy using example problems from engineering and the physical and biological sciences; and provides extensive MATLAB code, data for intuitive examples of key methods, and graphical presentations.
Foundations Of Complex Systems
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Author : G. Nicolis
language : en
Publisher: World Scientific
Release Date : 2007
Foundations Of Complex Systems written by G. Nicolis and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Complexity is emerging as a post-Newtonian paradigm for approaching a large body of phenomena of concern at the crossroads of physical, engineering, environmental, life and human sciences from a unifying point of view. This book outlines the foundations of modern complexity research as it arose from the cross-fertilization of ideas and tools from nonlinear science, statistical physics and numerical simulation. It is shown how these developments lead to an understanding, both qualitative and quantitative, of the complex systems encountered in nature and in everyday experience and, conversely, how natural complexity acts as a source of inspiration for progress at the fundamental level.
Synchronization And Triggering From Fracture To Earthquake Processes
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Author : Valerio de Rubeis
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-11
Synchronization And Triggering From Fracture To Earthquake Processes written by Valerio de Rubeis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-11 with Science categories.
Processes of synchronization and interaction play a very special role in different physical problems concerning the dynamics of the Earth’s interior; they are of particular importance in the study of seismic phenomena, and their complexity is strongly affected by the variety of geological structures and inhomogeneities of the medium that hamper the course of these processes and their intensity. The attempt to tackle these problems is a great challenge from experimental, observational and theoretical point of view. We present in this Monograph the theoretical and experimental results achieved in the frame of the European Project “Triggering and synchronization of seismic/ acoustic events by weak external forcing as a sign of approaching the critical point” (INTAS Ref. Nr 05-1000008-7889); in this Project, which was inspired by Professor Tamaz Chelidze, our aim was to give grounds for better understanding and interpretation of dynamical interactive processes of physical ?elds, both found in the laboratory experiments as well as in ?eld observations. One of the leading problems – related to synchronization and interaction of different physical ?elds in fracture processes concerns triggering and initiation of rupture and displa- ments within the Earth interior. From this point of view, the results from laboratory studies on synchronization and interaction and those found and involved in ?eld observations, helped to improve the theoretical background. Reversely, some of the presented new theoretical approaches have served to stimulate laboratory and ?eld studies.