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.
Download or read book Predictability of Complex Dynamical Systems written by Yurii A. Kravtsov and published by Springer. This book was released on 2012-01-06 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastic Modelling and Control written by M. H. A. Davis and published by Springer. This book was released on 1985 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to provide a unified treatment of input/output modelling and of control for discrete-time dynamical systems subject to random disturbances. The results presented are of wide applica bility in control engineering, operations research, econometric modelling and many other areas. There are two distinct approaches to mathematical modelling of physical systems: a direct analysis of the physical mechanisms that comprise the process, or a 'black box' approach based on analysis of input/output data. The second approach is adopted here, although of course the properties ofthe models we study, which within the limits of linearity are very general, are also relevant to the behaviour of systems represented by such models, however they are arrived at. The type of system we are interested in is a discrete-time or sampled-data system where the relation between input and output is (at least approximately) linear and where additive random dis turbances are also present, so that the behaviour of the system must be investigated by statistical methods. After a preliminary chapter summarizing elements of probability and linear system theory, we introduce in Chapter 2 some general linear stochastic models, both in input/output and state-space form. Chapter 3 concerns filtering theory: estimation of the state of a dynamical system from noisy observations. As well as being an important topic in its own right, filtering theory provides the link, via the so-called innovations representation, between input/output models (as identified by data analysis) and state-space models, as required for much contemporary control theory.
Download or read book Predictability of Complex Dynamical Systems written by James B. Kadtke and published by Springer. This book was released on 1996-10-04 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This practical guide to data analysis and algorithms addresses researchers and practitioners interested in modeling, prediction, and forecasting natural systems based on nonlinear dynamics. It explores many interesting topics in complex dynamical systems and shows how probabilistic techniques, such as signal and time-series analysis, financial and stochastic modeling, and political modeling can be used to predict them.
Download or read book Stochastic Equations for Complex Systems written by Stefan Heinz and published by Springer. This book was released on 2015-05-06 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical analyses and computational predictions of the behavior of complex systems are needed to effectively deal with weather and climate predictions, for example, and the optimal design of technical processes. Given the random nature of such systems and the recognized relevance of randomness, the equations used to describe such systems usually need to involve stochastics. The basic goal of this book is to introduce the mathematics and application of stochastic equations used for the modeling of complex systems. A first focus is on the introduction to different topics in mathematical analysis. A second focus is on the application of mathematical tools to the analysis of stochastic equations. A third focus is on the development and application of stochastic methods to simulate turbulent flows as seen in reality. This book is primarily oriented towards mathematics and engineering PhD students, young and experienced researchers, and professionals working in the area of stochastic differential equations and their applications. It contributes to a growing understanding of concepts and terminology used by mathematicians, engineers, and physicists in this relatively young and quickly expanding field.
Download or read book Introduction to Modeling and Analysis of Stochastic Systems written by V. G. Kulkarni and published by Springer. This book was released on 2010-11-03 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained review of all the relevant topics in probability theory. A software package called MAXIM, which runs on MATLAB, is made available for downloading. Vidyadhar G. Kulkarni is Professor of Operations Research at the University of North Carolina at Chapel Hill.
Download or read book The Art of Modeling Dynamic Systems written by Foster Morrison and published by Courier Corporation. This book was released on 2012-03-07 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text illustrates the roles of statistical methods, coordinate transformations, and mathematical analysis in mapping complex, unpredictable dynamical systems. It describes the benefits and limitations of the available modeling tools, showing engineers and scientists how any system can be rendered simpler and more predictable. Written by a well-known authority in the field, this volume employs practical examples and analogies to make models more meaningful. The more universal methods appear in considerable detail, and advanced dynamic principles feature easy-to-understand examples. The text draws careful distinctions between mathematical abstractions and observable realities. Additional topics include the role of pure mathematics, the limitations of numerical methods, forecasting in the presence of chaos and randomness, and dynamics without calculus. Specialized techniques and case histories are coordinated with a carefully selected and annotated bibliography. The original edition was a Library of Science Main Selection in May, 1991. This new Dover edition features corrections by the author and a new Preface.
Download or read book An Introduction to Stochastic Modeling written by Howard M. Taylor and published by Academic Press. This book was released on 2014-05-10 with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Stochastic Modeling, Revised Edition provides information pertinent to the standard concepts and methods of stochastic modeling. This book presents the rich diversity of applications of stochastic processes in the sciences. Organized into nine chapters, this book begins with an overview of diverse types of stochastic models, which predicts a set of possible outcomes weighed by their likelihoods or probabilities. This text then provides exercises in the applications of simple stochastic analysis to appropriate problems. Other chapters consider the study of general functions of independent, identically distributed, nonnegative random variables representing the successive intervals between renewals. This book discusses as well the numerous examples of Markov branching processes that arise naturally in various scientific disciplines. The final chapter deals with queueing models, which aid the design process by predicting system performance. This book is a valuable resource for students of engineering and management science. Engineers will also find this book useful.
Download or read book Tropical Intraseasonal Variability and the Stochastic Skeleton Method written by Andrew J. Majda and published by Springer Nature. This book was released on 2019-09-24 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this text, modern applied mathematics and physical insight are used to construct the simplest and first nonlinear dynamical model for the Madden-Julian oscillation (MJO), i.e. the stochastic skeleton model. This model captures the fundamental features of the MJO and offers a theoretical prediction of its structure, leading to new detailed methods to identify it in observational data. The text contributes to understanding and predicting intraseasonal variability, which remains a challenging task in contemporary climate, atmospheric, and oceanic science. In the tropics, the Madden-Julian oscillation (MJO) is the dominant component of intraseasonal variability. One of the strengths of this text is demonstrating how a blend of modern applied mathematical tools, including linear and nonlinear partial differential equations (PDEs), simple stochastic modeling, and numerical algorithms, have been used in conjunction with physical insight to create the model. These tools are also applied in developing several extensions of the model in order to capture additional features of the MJO, including its refined vertical structure and its interactions with the extratropics. This book is of interest to graduate students, postdocs, and senior researchers in pure and applied mathematics, physics, engineering, and climate, atmospheric, and oceanic science interested in turbulent dynamical systems as well as other complex systems.
Download or read book Stochastic Systems for Engineers written by John A. Borrie and published by . This book was released on 1992 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introduction to stochastic systems and an ordered presentation of techniques for computer modelling, filtering and control of these systems. The subject is developed with definition, formulae and explanations but without detailed mathematical proofs.
Download or read book Modeling and Analysis of Stochastic Systems written by Vidyadhar G. Kulkarni and published by CRC Press. This book was released on 2009-12-18 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the author's more than 25 years of teaching experience, Modeling and Analysis of Stochastic Systems, Second Edition covers the most important classes of stochastic processes used in the modeling of diverse systems, from supply chains and inventory systems to genetics and biological systems. For each class of stochastic process, the text includes its definition, characterization, applications, transient and limiting behavior, first passage times, and cost/reward models. Along with reorganizing the material, this edition revises and adds new exercises and examples. New to the second edition: a new chapter on diffusion processes that gives an accessible and non-measure-theoretic treatment with applications to finance; a more streamlined, application-oriented approach to renewal, regenerative, and Markov regenerative processes; and, two appendices that collect relevant results from analysis and differential and difference equations. Rather than offer special tricks that work in specific problems, this book provides thorough coverage of general tools that enable the solution and analysis of stochastic models. After mastering the material in the text, students will be well-equipped to build and analyze useful stochastic models for various situations. A collection of MATLAB[registered]-based programs can be downloaded from the author's website and a solutions manual is available for qualifying instructors.
Download or read book Recent Development in Stochastic Dynamics and Stochastic Analysis written by Jinqiao Duan and published by World Scientific. This book was released on 2010 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic dynamical systems and stochastic analysis are of great interests not only to mathematicians but also scientists in other areas. Stochastic dynamical systems tools for modeling and simulation are highly demanded in investigating complex phenomena in, for example, environmental and geophysical sciences, materials science, life sciences, physical and chemical sciences, finance and economics. The volume reflects an essentially timely and interesting subject and offers reviews on the recent and new developments in stochastic dynamics and stochastic analysis, and also some possible future research directions. Presenting a dozen chapters of survey papers and research by leading experts in the subject, the volume is written with a wide audience in mind ranging from graduate students, junior researchers to professionals of other specializations who are interested in the subject.
Download or read book Modeling and Analysis of Stochastic Systems Second Edition Solutions Manual written by Taylor & Francis Group and published by . This book was released on 2009-12-11 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This practical and accessible text enables readers from engineering, business, operations research, public policy and computer science to analyze stochastic systems. Emphasizing the modeling of real-life situations with stochastic elements and analyzing the resulting stochastic model, it presents the major cases of useful stochastic processes-discrete and continuous time Markov chains, renewal processes, regenerative processes, and Markov regenerative processes. The author provides reader-friendly yet rigorous coverage. He follows a set pattern of development for each class of stochastic processes and introduces Markov chains before renewal processes, so that readers can begin modeling systems early. He demonstrates both numerical and analytical solution methods in detail and dedicates a separate chapter to queueing applications. Modeling and Analysis of Stochastic Systems includes numerous worked examples and exercises, conveniently categorized as modeling, computational, or conceptual and making difficult concepts easy to grasp. Taking a practical approach to working with stochastic models, this book helps readers to model and analyze the increasingly complex and interdependent systems made possible by recent advances.
Download or read book Linear Stochastic Systems written by Peter E. Caines and published by SIAM. This book was released on 2018-06-12 with total page 874 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear Stochastic Systems, originally published in 1988, is today as comprehensive a reference to the theory of linear discrete-time-parameter systems as ever. Its most outstanding feature is the unified presentation, including both input-output and state space representations of stochastic linear systems, together with their interrelationships. The author first covers the foundations of linear stochastic systems and then continues through to more sophisticated topics including the fundamentals of stochastic processes and the construction of stochastic systems; an integrated exposition of the theories of prediction, realization (modeling), parameter estimation, and control; and a presentation of stochastic adaptive control theory. Written in a clear, concise manner and accessible to graduate students, researchers, and teachers, this classic volume also includes background material to make it self-contained and has complete proofs for all the principal results of the book. Furthermore, this edition includes many corrections of errata collected over the years.
Download or read book Stochastic Pdes And Modelling Of Multiscale Complex System written by Wang Wei and published by World Scientific. This book was released on 2019-05-07 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is devoted to original research results and survey articles reviewing recent developments in reduction for stochastic PDEs with multiscale as well as application to science and technology, and to present some future research direction. This volume includes a dozen chapters by leading experts in the area, with a broad audience in mind. It should be accessible to graduate students, junior researchers and other professionals who are interested in the subject. We also take this opportunity to celebrate the contributions of Professor Anthony J Roberts, an internationally leading figure on the occasion of his 60th years birthday in 2017.
Download or read book Analysis and Data Based Reconstruction of Complex Nonlinear Dynamical Systems written by M. Reza Rahimi Tabar and published by . This book was released on 2019 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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".
