Predictability Of Complex Dynamical Systems

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Predictability of Complex Dynamical Systems

Author : Yurii A. Kravtsov
Publisher : Springer Science & Business Media
ISBN 13 : 3642802540
Total Pages : 233 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Predictability of Complex Dynamical Systems by : Yurii A. Kravtsov

Download or read book Predictability of Complex Dynamical Systems written by Yurii A. Kravtsov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book book for researchers and practitioners interested in modeling, prediction and forecasting of natural systems based on nonlinear dynamics. It is a practical guide to data analysis and to the development of algorithms, especially for complex systems. Topics such as the characterization of nonlinear correlations in data as dynamical systems, reconstruction of dynamical models from data, nonlinear noise reduction and the limits of predicatability are discussed. The chapters are written by leading experts and consider practical problems such as signal and time series analysis, biomedical data analysis, financial analysis, stochastic modeling, human evolution, and political modeling. The book includes new methods for nonlinear filtering of complex signals, new algorithms for signal classification, and the concept of the "Global Brain".

Predictability of Chaotic Dynamics

Author : Juan C. Vallejo
Publisher : Springer
ISBN 13 : 3319518933
Total Pages : 147 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Predictability of Chaotic Dynamics by : Juan C. Vallejo

Download or read book Predictability of Chaotic Dynamics written by Juan C. Vallejo and published by Springer. This book was released on 2017-03-27 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is primarily concerned with the computational aspects of predictability of dynamical systems – in particular those where observation, modeling and computation are strongly interdependent. Unlike with physical systems under control in laboratories, for instance in celestial mechanics, one is confronted with the observation and modeling of systems without the possibility of altering the key parameters of the objects studied. Therefore, the numerical simulations offer an essential tool for analyzing these systems. With the widespread use of computer simulations to solve complex dynamical systems, the reliability of the numerical calculations is of ever-increasing interest and importance. This reliability is directly related to the regularity and instability properties of the modeled flow. In this interdisciplinary scenario, the underlying physics provide the simulated models, nonlinear dynamics provides their chaoticity and instability properties, and the computer sciences provide the actual numerical implementation. This book introduces and explores precisely this link between the models and their predictability characterization based on concepts derived from the field of nonlinear dynamics, with a focus on the finite-time Lyapunov exponents approach. The method is illustrated using a number of well-known continuous dynamical systems, including the Contopoulos, Hénon-Heiles and Rössler systems. To help students and newcomers quickly learn to apply these techniques, the appendix provides descriptions of the algorithms used throughout the text and details how to implement them in order to solve a given continuous dynamical system.

Foundations of Complex Systems

Author : G. Nicolis
Publisher : World Scientific
ISBN 13 : 9814366617
Total Pages : 384 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Foundations of Complex Systems by : G. Nicolis

Download or read book Foundations of Complex Systems written by G. Nicolis and published by World Scientific. This book was released on 2012 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained presentation of the physical and mathematical laws governing complex systems. Complex systems arising in natural, engineering, environmental, life and social sciences are approached from a unifying point of view using an array of methodologies such as microscopic and macroscopic level formulations, deterministic and probabilistic tools, modeling and simulation. The book can be used as a textbook by graduate students, researchers and teachers in science, as well as non-experts who wish to have an overview of one of the most open, markedly interdisciplinary and fast-growing branches of present-day science.

Dynamics Of Complex Systems

Author : Yaneer Bar-yam
Publisher : CRC Press
ISBN 13 : 0429717598
Total Pages : 866 pages
Book Rating : 4.4/5 (297 download)

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Book Synopsis Dynamics Of Complex Systems by : Yaneer Bar-yam

Download or read book Dynamics Of Complex Systems written by Yaneer Bar-yam and published by CRC Press. This book was released on 2019-03-04 with total page 866 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to develop models and modeling techniques that are useful when applied to all complex systems. It adopts both analytic tools and computer simulation. The book is intended for students and researchers with a variety of backgrounds.

Nonlinear Dynamics and Statistics

Author : Alistair I. Mees
Publisher : Springer Science & Business Media
ISBN 13 : 9780817641634
Total Pages : 490 pages
Book Rating : 4.6/5 (416 download)

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Book Synopsis Nonlinear Dynamics and Statistics by : Alistair I. Mees

Download or read book Nonlinear Dynamics and Statistics written by Alistair I. Mees and published by Springer Science & Business Media. This book was released on 2001-01-25 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the state of the art in nonlinear dynamical reconstruction theory. The chapters are based upon a workshop held at the Isaac Newton Institute, Cambridge University, UK, in late 1998. The book's chapters present theory and methods topics by leading researchers in applied and theoretical nonlinear dynamics, statistics, probability, and systems theory. Features and topics: * disentangling uncertainty and error: the predictability of nonlinear systems * achieving good nonlinear models * delay reconstructions: dynamics vs. statistics * introduction to Monte Carlo Methods for Bayesian Data Analysis * latest results in extracting dynamical behavior via Markov Models * data compression, dynamics and stationarity Professionals, researchers, and advanced graduates in nonlinear dynamics, probability, optimization, and systems theory will find the book a useful resource and guide to current developments in the subject.

Foundations Of Complex Systems: Nonlinear Dynamics, Statistical Physics, Information And Prediction

Author : Gregoire Nicolis
Publisher : World Scientific
ISBN 13 : 9814476943
Total Pages : 343 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Foundations Of Complex Systems: Nonlinear Dynamics, Statistical Physics, Information And Prediction by : Gregoire Nicolis

Download or read book Foundations Of Complex Systems: Nonlinear Dynamics, Statistical Physics, Information And Prediction written by Gregoire Nicolis and published by World Scientific. This book was released on 2007-09-03 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematics of Complexity and Dynamical Systems

Author : Robert A. Meyers
Publisher : Springer Science & Business Media
ISBN 13 : 1461418054
Total Pages : 1885 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Mathematics of Complexity and Dynamical Systems by : Robert A. Meyers

Download or read book Mathematics of Complexity and Dynamical Systems written by Robert A. Meyers and published by Springer Science & Business Media. This book was released on 2011-10-05 with total page 1885 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

Stochastic Methods for Modeling and Predicting Complex Dynamical Systems

Author : Nan Chen
Publisher : Springer Nature
ISBN 13 : 3031222490
Total Pages : 208 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Stochastic Methods for Modeling and Predicting Complex Dynamical Systems by : Nan Chen

Download or read book Stochastic Methods for Modeling and Predicting Complex Dynamical Systems written by Nan Chen and published by Springer Nature. This book was released on 2023-03-13 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book enables readers to understand, model, and predict complex dynamical systems using new methods with stochastic tools. The author presents a unique combination of qualitative and quantitative modeling skills, novel efficient computational methods, rigorous mathematical theory, as well as physical intuitions and thinking. An emphasis is placed on the balance between computational efficiency and modeling accuracy, providing readers with ideas to build useful models in practice. Successful modeling of complex systems requires a comprehensive use of qualitative and quantitative modeling approaches, novel efficient computational methods, physical intuitions and thinking, as well as rigorous mathematical theories. As such, mathematical tools for understanding, modeling, and predicting complex dynamical systems using various suitable stochastic tools are presented. Both theoretical and numerical approaches are included, allowing readers to choose suitable methods in different practical situations. The author provides practical examples and motivations when introducing various mathematical and stochastic tools and merges mathematics, statistics, information theory, computational science, and data science. In addition, the author discusses how to choose and apply suitable mathematical tools to several disciplines including pure and applied mathematics, physics, engineering, neural science, material science, climate and atmosphere, ocean science, and many others. Readers will not only learn detailed techniques for stochastic modeling and prediction, but will develop their intuition as well. Important topics in modeling and prediction including extreme events, high-dimensional systems, and multiscale features are discussed.

Predictive Approaches to Control of Complex Systems

Author : Gorazd Karer
Publisher : Springer
ISBN 13 : 9783642339486
Total Pages : 260 pages
Book Rating : 4.3/5 (394 download)

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Book Synopsis Predictive Approaches to Control of Complex Systems by : Gorazd Karer

Download or read book Predictive Approaches to Control of Complex Systems written by Gorazd Karer and published by Springer. This book was released on 2012-09-21 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: A predictive control algorithm uses a model of the controlled system to predict the system behavior for various input scenarios and determines the most appropriate inputs accordingly. Predictive controllers are suitable for a wide range of systems; therefore, their advantages are especially evident when dealing with relatively complex systems, such as nonlinear, constrained, hybrid, multivariate systems etc. However, designing a predictive control strategy for a complex system is generally a difficult task, because all relevant dynamical phenomena have to be considered. Establishing a suitable model of the system is an essential part of predictive control design. Classic modeling and identification approaches based on linear-systems theory are generally inappropriate for complex systems; hence, models that are able to appropriately consider complex dynamical properties have to be employed in a predictive control algorithm. This book first introduces some modeling frameworks, which can encompass the most frequently encountered complex dynamical phenomena and are practically applicable in the proposed predictive control approaches. Furthermore, unsupervised learning methods that can be used for complex-system identification are treated. Finally, several useful predictive control algorithms for complex systems are proposed and their particular advantages and drawbacks are discussed. The presented modeling, identification and control approaches are complemented by illustrative examples. The book is aimed towards researches and postgraduate students interested in modeling, identification and control, as well as towards control engineers needing practically usable advanced control methods for complex systems.

Philosophy of Complex Systems

Author :
Publisher : Elsevier
ISBN 13 : 0080931227
Total Pages : 951 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Philosophy of Complex Systems by :

Download or read book Philosophy of Complex Systems written by and published by Elsevier. This book was released on 2011-05-23 with total page 951 pages. Available in PDF, EPUB and Kindle. Book excerpt: The domain of nonlinear dynamical systems and its mathematical underpinnings has been developing exponentially for a century, the last 35 years seeing an outpouring of new ideas and applications and a concomitant confluence with ideas of complex systems and their applications from irreversible thermodynamics. A few examples are in meteorology, ecological dynamics, and social and economic dynamics. These new ideas have profound implications for our understanding and practice in domains involving complexity, predictability and determinism, equilibrium, control, planning, individuality, responsibility and so on.Our intention is to draw together in this volume, we believe for the first time, a comprehensive picture of the manifold philosophically interesting impacts of recent developments in understanding nonlinear systems and the unique aspects of their complexity. The book will focus specifically on the philosophical concepts, principles, judgments and problems distinctly raised by work in the domain of complex nonlinear dynamical systems, especially in recent years. -Comprehensive coverage of all main theories in the philosophy of Complex Systems -Clearly written expositions of fundamental ideas and concepts -Definitive discussions by leading researchers in the field -Summaries of leading-edge research in related fields are also included

Applications of Nonlinear Dynamics

Author : Visarath In
Publisher : Springer Science & Business Media
ISBN 13 : 3540856323
Total Pages : 464 pages
Book Rating : 4.5/5 (48 download)

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Book Synopsis Applications of Nonlinear Dynamics by : Visarath In

Download or read book Applications of Nonlinear Dynamics written by Visarath In and published by Springer Science & Business Media. This book was released on 2009-02-11 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ?eld of applied nonlinear dynamics has attracted scientists and engineers across many different disciplines to develop innovative ideas and methods to study c- plex behavior exhibited by relatively simple systems. Examples include: population dynamics, ?uidization processes, applied optics, stochastic resonance, ?ocking and ?ightformations,lasers,andmechanicalandelectricaloscillators. Acommontheme among these and many other examples is the underlying universal laws of nonl- ear science that govern the behavior, in space and time, of a given system. These laws are universal in the sense that they transcend the model-speci?c features of a system and so they can be readily applied to explain and predict the behavior of a wide ranging phenomena, natural and arti?cial ones. Thus the emphasis in the past decades has been in explaining nonlinear phenomena with signi?cantly less att- tion paid to exploiting the rich behavior of nonlinear systems to design and fabricate new devices that can operate more ef?ciently. Recently, there has been a series of meetings on topics such as Experimental Chaos, Neural Coding, and Stochastic Resonance, which have brought together many researchers in the ?eld of nonlinear dynamics to discuss, mainly, theoretical ideas that may have the potential for further implementation. In contrast, the goal of the 2007 ICAND (International Conference on Applied Nonlinear Dynamics) was focused more sharply on the implementation of theoretical ideas into actual - vices and systems.

Complex Dynamical Systems in Education

Author : Matthijs Koopmans
Publisher : Springer
ISBN 13 : 3319275771
Total Pages : 416 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Complex Dynamical Systems in Education by : Matthijs Koopmans

Download or read book Complex Dynamical Systems in Education written by Matthijs Koopmans and published by Springer. This book was released on 2016-02-19 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book capitalizes on the developments in dynamical systems and education by presenting some of the most recent advances in this area in seventeen non-overlapping chapters. The first half of the book discusses the conceptual framework of complex dynamical systems and its applicability to educational processes. The second half presents a set of empirical studies that that illustrate the use of various research methodologies to investigate complex dynamical processes in education, and help the reader appreciate what we learn about dynamical processes in education from using these approaches.

From Instability to Intelligence

Author : Michail Zak
Publisher : Springer Science & Business Media
ISBN 13 : 3540691219
Total Pages : 559 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis From Instability to Intelligence by : Michail Zak

Download or read book From Instability to Intelligence written by Michail Zak and published by Springer Science & Business Media. This book was released on 2008-12-11 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: So far as the laws of mathematics refer to reality, they are not certain. And so far as they are certain, they do not refer to reality. -A. Einstein The word "instability" in day-to-day language is associated with some thing going wrong or being abnormal: exponential growth of cancer cells, irrational behavior of a patient, collapse of a structure, etc. This book, however, is about "good" instabilities, which lead to change, evolution, progress, creativity, and intelligence; they explain the paradox of irreversi bility in thermodynamics, the phenomena of chaos and turbulence in clas sical mechanics, and non-deterministic (multi-choice) behavior in biological and social systems. The concept of instability is an attribute of dynamical models that de scribe change in time of physical parameters, biological or social events, etc. Each dynamical model has a certain sensitivity to small changes or "errors" in initial values of its variables. These errors may grow in time, and if such growth is of an exponential rate, the behavior of the variable is defined as unstable. However, the overall effect of an unstable variable upon the dynamical system is not necessarily destructive. Indeed, there al ways exists such a group of variables that do not contribute to the energy of the system. In mechanics such variables are called ignorable or cyclic.

Prediction and Characterization of Complex Systems

Author :
Publisher :
ISBN 13 :
Total Pages : 8 pages
Book Rating : 4.:/5 (684 download)

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Book Synopsis Prediction and Characterization of Complex Systems by :

Download or read book Prediction and Characterization of Complex Systems written by and published by . This book was released on 1996 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex systems are difficult to characterize and to simulate. By considering a series of explicit systems, through experiments and analysis, this project has shown that dynamical systems can be used to model complex systems. A complex dynamical system requires an exponential amount of computer work to simulate accurately. Direct methods are not practical and it is only by an hierarchical approach that one can gain control over the exponential behavior. This allows the development of efficient methods to study fluid flow and to simulate biological systems. There are two steps in the hierarchical approach. First, one must characterize the complex system as a collection of large domains or objects that have their own forms of interactions. This is done by considering coherent structures, such as solitons, spirals, and propagating fronts and determining their interactions. Second, one must be able to predict the properties of the resulting low-dimensional dynamical system. This is accomplished by an understanding of the topology of the orbits of the dynamical system. The coherent structure description was carried out in fluid and reaction diffusion systems. It was shown that very simple models from statistical mechanics could characterize a rotating Rayleigh-Benard system and that patters in reaction-diffusion systems are well described by soliton-like solutions. The studies of dynamical systems showed that simple characterizations of the phase space can be used to determine long time bounds. Also, that periodic orbit theory can be used to demonstrate that Monte Carlo simulations will converge to incorrect results.

Optimal Control and Forecasting of Complex Dynamical Systems

Author : Ilya Grigorenko
Publisher : World Scientific
ISBN 13 : 9812774246
Total Pages : 213 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Optimal Control and Forecasting of Complex Dynamical Systems by : Ilya Grigorenko

Download or read book Optimal Control and Forecasting of Complex Dynamical Systems written by Ilya Grigorenko and published by World Scientific. This book was released on 2006 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: The core of classical economic analysis represented by William Petty and Adam Smith concentrated on the field of development economics. This classical footing of the study of development is different from the neoclassical perspective in two important respects: it focuses on division of labor as the driving force of development, and it emphasizes the role of the market (the "invisible hand") in exploiting productivity gains that are derived from division of labor. However these aspects have received little attention in the body of literature that represents the modern field of development economics - which largely represents the neoclassical application of marginalism. A notable exception is research that utilizes inframarginal analysis of individuals' networking decisions in an attempt to formalize the classical mechanisms that drive division of labor. This book is a first attempt to collect relevant key contributions and is intended for active researchers in the field of development economics.

Analysis and Control of Complex Dynamical Systems

Author : Kazuyuki Aihara
Publisher : Springer
ISBN 13 : 4431550135
Total Pages : 215 pages
Book Rating : 4.4/5 (315 download)

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Book Synopsis Analysis and Control of Complex Dynamical Systems by : Kazuyuki Aihara

Download or read book Analysis and Control of Complex Dynamical Systems written by Kazuyuki Aihara and published by Springer. This book was released on 2015-03-20 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first to report on theoretical breakthroughs on control of complex dynamical systems developed by collaborative researchers in the two fields of dynamical systems theory and control theory. As well, its basic point of view is of three kinds of complexity: bifurcation phenomena subject to model uncertainty, complex behavior including periodic/quasi-periodic orbits as well as chaotic orbits, and network complexity emerging from dynamical interactions between subsystems. Analysis and Control of Complex Dynamical Systems offers a valuable resource for mathematicians, physicists, and biophysicists, as well as for researchers in nonlinear science and control engineering, allowing them to develop a better fundamental understanding of the analysis and control synthesis of such complex systems.

Complex and Chaotic Nonlinear Dynamics

Author : Thierry Vialar
Publisher : Springer Science & Business Media
ISBN 13 : 3540859780
Total Pages : 752 pages
Book Rating : 4.5/5 (48 download)

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Book Synopsis Complex and Chaotic Nonlinear Dynamics by : Thierry Vialar

Download or read book Complex and Chaotic Nonlinear Dynamics written by Thierry Vialar and published by Springer Science & Business Media. This book was released on 2009-04-26 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex dynamics constitute a growing and increasingly important area as they offer a strong potential to explain and formalize natural, physical, financial and economic phenomena. This book pursues the ambitious goal to bring together an extensive body of knowledge regarding complex dynamics from various academic disciplines. Beyond its focus on economics and finance, including for instance the evolution of macroeconomic growth models towards nonlinear structures as well as signal processing applications to stock markets, fundamental parts of the book are devoted to the use of nonlinear dynamics in mathematics, statistics, signal theory and processing. Numerous examples and applications, almost 700 illustrations and numerical simulations based on the use of Matlab make the book an essential reference for researchers and students from many different disciplines who are interested in the nonlinear field. An appendix recapitulates the basic mathematical concepts required to use the book.