Dynamics Of Stochastic Systems

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Dynamics of Stochastic Systems

Author : Valery I. Klyatskin
Publisher : Elsevier
ISBN 13 : 008050485X
Total Pages : 211 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Dynamics of Stochastic Systems by : Valery I. Klyatskin

Download or read book Dynamics of Stochastic Systems written by Valery I. Klyatskin and published by Elsevier. This book was released on 2005-03-17 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fluctuating parameters appear in a variety of physical systems and phenomena. They typically come either as random forces/sources, or advecting velocities, or media (material) parameters, like refraction index, conductivity, diffusivity, etc. The well known example of Brownian particle suspended in fluid and subjected to random molecular bombardment laid the foundation for modern stochastic calculus and statistical physics. Other important examples include turbulent transport and diffusion of particle-tracers (pollutants), or continuous densities (''oil slicks''), wave propagation and scattering in randomly inhomogeneous media, for instance light or sound propagating in the turbulent atmosphere.Such models naturally render to statistical description, where the input parameters and solutions are expressed by random processes and fields.The fundamental problem of stochastic dynamics is to identify the essential characteristics of system (its state and evolution), and relate those to the input parameters of the system and initial data.This raises a host of challenging mathematical issues. One could rarely solve such systems exactly (or approximately) in a closed analytic form, and their solutions depend in a complicated implicit manner on the initial-boundary data, forcing and system's (media) parameters . In mathematical terms such solution becomes a complicated "nonlinear functional" of random fields and processes.Part I gives mathematical formulation for the basic physical models of transport, diffusion, propagation and develops some analytic tools.Part II sets up and applies the techniques of variational calculus and stochastic analysis, like Fokker-Plank equation to those models, to produce exact or approximate solutions, or in worst case numeric procedures. The exposition is motivated and demonstrated with numerous examples.Part III takes up issues for the coherent phenomena in stochastic dynamical systems, described by ordinary and partial differential equations, like wave propagation in randomly layered media (localization), turbulent advection of passive tracers (clustering).Each chapter is appended with problems the reader to solve by himself (herself), which will be a good training for independent investigations.·This book is translation from Russian and is completed with new principal results of recent research.·The book develops mathematical tools of stochastic analysis, and applies them to a wide range of physical models of particles, fluids, and waves.·Accessible to a broad audience with general background in mathematical physics, but no special expertise in stochastic analysis, wave propagation or turbulence

Nonlinear Dynamics of Chaotic and Stochastic Systems

Author : Vadim S. Anishchenko
Publisher : Springer Science & Business Media
ISBN 13 : 3540381686
Total Pages : 463 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Nonlinear Dynamics of Chaotic and Stochastic Systems by : Vadim S. Anishchenko

Download or read book Nonlinear Dynamics of Chaotic and Stochastic Systems written by Vadim S. Anishchenko and published by Springer Science & Business Media. This book was released on 2007-07-20 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present an improved and enlarged version of our book Nonlinear - namics of Chaotic and Stochastic Systems published by Springer in 2002. Basically, the new edition of the book corresponds to its ?rst version. While preparingthiseditionwemadesomeclari?cationsinseveralsectionsandalso corrected the misprints noticed in some formulas. Besides, three new sections have been added to Chapter 2. They are “Statistical Properties of Dynamical Chaos,” “E?ects of Synchronization in Extended Self-Sustained Oscillatory Systems,” and “Synchronization in Living Systems.” The sections indicated re?ect the most interesting results obtained by the authors after publication of the ?rst edition. We hope that the new edition of the book will be of great interest for a widesectionofreaderswhoarealreadyspecialistsorthosewhoarebeginning research in the ?elds of nonlinear oscillation and wave theory, dynamical chaos, synchronization, and stochastic process theory. Saratov, Berlin, and St. Louis V.S. Anishchenko November 2006 A.B. Neiman T.E. Vadiavasova V.V. Astakhov L. Schimansky-Geier Preface to the First Edition Thisbookisdevotedtotheclassicalbackgroundandtocontemporaryresults on nonlinear dynamics of deterministic and stochastic systems. Considerable attentionisgiventothee?ectsofnoiseonvariousregimesofdynamicsystems with noise-induced order. On the one hand, there exists a rich literature of excellent books on n- linear dynamics and chaos; on the other hand, there are many marvelous monographs and textbooks on the statistical physics of far-from-equilibrium andstochasticprocesses.Thisbookisanattempttocombinetheapproachof nonlinear dynamics based on the deterministic evolution equations with the approach of statistical physics based on stochastic or kinetic equations. One of our main aims is to show the important role of noise in the organization and properties of dynamic regimes of nonlinear dissipative systems.

Stochastic Dynamics and Control

Author : Jian-Qiao Sun
Publisher : Elsevier
ISBN 13 : 0080463983
Total Pages : 427 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Stochastic Dynamics and Control by : Jian-Qiao Sun

Download or read book Stochastic Dynamics and Control written by Jian-Qiao Sun and published by Elsevier. This book was released on 2006-08-10 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a result of many years of author's research and teaching on random vibration and control. It was used as lecture notes for a graduate course. It provides a systematic review of theory of probability, stochastic processes, and stochastic calculus. The feedback control is also reviewed in the book. Random vibration analyses of SDOF, MDOF and continuous structural systems are presented in a pedagogical order. The application of the random vibration theory to reliability and fatigue analysis is also discussed. Recent research results on fatigue analysis of non-Gaussian stress processes are also presented. Classical feedback control, active damping, covariance control, optimal control, sliding control of stochastic systems, feedback control of stochastic time-delayed systems, and probability density tracking control are studied. Many control results are new in the literature and included in this book for the first time. The book serves as a reference to the engineers who design and maintain structures subject to harsh random excitations including earthquakes, sea waves, wind gusts, and aerodynamic forces, and would like to reduce the damages of structural systems due to random excitations.· Comprehensive review of probability theory, and stochastic processes· Random vibrations· Structural reliability and fatigue, Non-Gaussian fatigue· Monte Carlo methods· Stochastic calculus and engineering applications· Stochastic feedback controls and optimal controls· Stochastic sliding mode controls· Feedback control of stochastic time-delayed systems· Probability density tracking control

Stochastic Dynamics of Structures

Author : Jie Li
Publisher : John Wiley & Sons
ISBN 13 : 0470824255
Total Pages : 426 pages
Book Rating : 4.4/5 (78 download)

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Book Synopsis Stochastic Dynamics of Structures by : Jie Li

Download or read book Stochastic Dynamics of Structures written by Jie Li and published by John Wiley & Sons. This book was released on 2009-07-23 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Stochastic Dynamics of Structures, Li and Chen present a unified view of the theory and techniques for stochastic dynamics analysis, prediction of reliability, and system control of structures within the innovative theoretical framework of physical stochastic systems. The authors outline the fundamental concepts of random variables, stochastic process and random field, and orthogonal expansion of random functions. Readers will gain insight into core concepts such as stochastic process models for typical dynamic excitations of structures, stochastic finite element, and random vibration analysis. Li and Chen also cover advanced topics, including the theory of and elaborate numerical methods for probability density evolution analysis of stochastic dynamical systems, reliability-based design, and performance control of structures. Stochastic Dynamics of Structures presents techniques for researchers and graduate students in a wide variety of engineering fields: civil engineering, mechanical engineering, aerospace and aeronautics, marine and offshore engineering, ship engineering, and applied mechanics. Practicing engineers will benefit from the concise review of random vibration theory and the new methods introduced in the later chapters. "The book is a valuable contribution to the continuing development of the field of stochastic structural dynamics, including the recent discoveries and developments by the authors of the probability density evolution method (PDEM) and its applications to the assessment of the dynamic reliability and control of complex structures through the equivalent extreme-value distribution." —A. H-S. Ang, NAE, Hon. Mem. ASCE, Research Professor, University of California, Irvine, USA "The authors have made a concerted effort to present a responsible and even holistic account of modern stochastic dynamics. Beyond the traditional concepts, they also discuss theoretical tools of recent currency such as the Karhunen-Loeve expansion, evolutionary power spectra, etc. The theoretical developments are properly supplemented by examples from earthquake, wind, and ocean engineering. The book is integrated by also comprising several useful appendices, and an exhaustive list of references; it will be an indispensable tool for students, researchers, and practitioners endeavoring in its thematic field." —Pol Spanos, NAE, Ryon Chair in Engineering, Rice University, Houston, USA

Stochastic Dynamics

Author : Hans Crauel
Publisher : Springer Science & Business Media
ISBN 13 : 0387226559
Total Pages : 457 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Stochastic Dynamics by : Hans Crauel

Download or read book Stochastic Dynamics written by Hans Crauel and published by Springer Science & Business Media. This book was released on 2007-12-14 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on the mathematical description of stochastic dynamics in discrete as well as in continuous time, this book investigates such dynamical phenomena as perturbations, bifurcations and chaos. It also introduces new ideas for the exploration of infinite dimensional systems, in particular stochastic partial differential equations. Example applications are presented from biology, chemistry and engineering, while describing numerical treatments of stochastic systems.

Elements Of Stochastic Dynamics

Author : Guo-qiang Cai
Publisher : World Scientific Publishing Company
ISBN 13 : 9814723347
Total Pages : 552 pages
Book Rating : 4.8/5 (147 download)

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Book Synopsis Elements Of Stochastic Dynamics by : Guo-qiang Cai

Download or read book Elements Of Stochastic Dynamics written by Guo-qiang Cai and published by World Scientific Publishing Company. This book was released on 2016-08-11 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic dynamics has been a subject of interest since the early 20th Century. Since then, much progress has been made in this field of study, and many modern applications for it have been found in fields such as physics, chemistry, biology, ecology, economy, finance, and many branches of engineering including Mechanical, Ocean, Civil, Bio, and Earthquake Engineering.Elements of Stochastic Dynamics aims to meet the growing need to understand and master the subject by introducing fundamentals to researchers who want to explore stochastic dynamics in their fields and serving as a textbook for graduate students in various areas involving stochastic uncertainties. All topics within are presented from an application approach, and may thus be more appealing to users without a background in pure Mathematics. The book describes the basic concepts and theories of random variables and stochastic processes in detail; provides various solution procedures for systems subjected to stochastic excitations; introduces stochastic stability and bifurcation; and explores failures of stochastic systems. The book also incorporates some latest research results in modeling stochastic processes; in reducing the system degrees of freedom; and in solving nonlinear problems. The book also provides numerical simulation procedures of widely-used random variables and stochastic processes.A large number of exercise problems are included in the book to aid the understanding of the concepts and theories, and may be used for as course homework.

Stochastic Dynamical Systems

Author : Josef Honerkamp
Publisher : John Wiley & Sons
ISBN 13 : 9780471188346
Total Pages : 558 pages
Book Rating : 4.1/5 (883 download)

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Book Synopsis Stochastic Dynamical Systems by : Josef Honerkamp

Download or read book Stochastic Dynamical Systems written by Josef Honerkamp and published by John Wiley & Sons. This book was released on 1996-12-17 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique volume introduces the reader to the mathematical language for complex systems and is ideal for students who are starting out in the study of stochastical dynamical systems. Unlike other books in the field it covers a broad array of stochastic and statistical methods.

Effective Dynamics of Stochastic Partial Differential Equations

Author : Jinqiao Duan
Publisher : Elsevier
ISBN 13 : 0128012692
Total Pages : 283 pages
Book Rating : 4.1/5 (28 download)

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Book Synopsis Effective Dynamics of Stochastic Partial Differential Equations by : Jinqiao Duan

Download or read book Effective Dynamics of Stochastic Partial Differential Equations written by Jinqiao Duan and published by Elsevier. This book was released on 2014-03-06 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Effective Dynamics of Stochastic Partial Differential Equations focuses on stochastic partial differential equations with slow and fast time scales, or large and small spatial scales. The authors have developed basic techniques, such as averaging, slow manifolds, and homogenization, to extract effective dynamics from these stochastic partial differential equations. The authors' experience both as researchers and teachers enable them to convert current research on extracting effective dynamics of stochastic partial differential equations into concise and comprehensive chapters. The book helps readers by providing an accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations. Each chapter also includes exercises and problems to enhance comprehension. - New techniques for extracting effective dynamics of infinite dimensional dynamical systems under uncertainty - Accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations - Solutions or hints to all Exercises

An Introduction to Stochastic Dynamics

Author : Jinqiao Duan
Publisher : Cambridge University Press
ISBN 13 : 1107075394
Total Pages : 313 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis An Introduction to Stochastic Dynamics by : Jinqiao Duan

Download or read book An Introduction to Stochastic Dynamics written by Jinqiao Duan and published by Cambridge University Press. This book was released on 2015-04-13 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction for applied mathematicians to concepts and techniques for describing, quantifying, and understanding dynamics under uncertainty.

Lectures on Dynamics of Stochastic Systems

Author : Valery I. Klyatskin
Publisher : Elsevier
ISBN 13 : 0123849675
Total Pages : 411 pages
Book Rating : 4.1/5 (238 download)

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Book Synopsis Lectures on Dynamics of Stochastic Systems by : Valery I. Klyatskin

Download or read book Lectures on Dynamics of Stochastic Systems written by Valery I. Klyatskin and published by Elsevier. This book was released on 2010-09-09 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fluctuating parameters appear in a variety of physical systems and phenomena. They typically come either as random forces/sources, or advecting velocities, or media (material) parameters, like refraction index, conductivity, diffusivity, etc. Models naturally render to statistical description, where random processes and fields express the input parameters and solutions. The fundamental problem of stochastic dynamics is to identify the essential characteristics of the system (its state and evolution), and relate those to the input parameters of the system and initial data. This book is a revised and more comprehensive version of Dynamics of Stochastic Systems. Part I provides an introduction to the topic. Part II is devoted to the general theory of statistical analysis of dynamic systems with fluctuating parameters described by differential and integral equations. Part III deals with the analysis of specific physical problems associated with coherent phenomena. - A comprehensive update of Dynamics of Stochastic Systems - Develops mathematical tools of stochastic analysis and applies them to a wide range of physical models of particles, fluids and waves - Includes problems for the reader to solve

Stochastic Dynamics for Systems Biology

Author : Christian Mazza
Publisher : CRC Press
ISBN 13 : 1466514949
Total Pages : 274 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Stochastic Dynamics for Systems Biology by : Christian Mazza

Download or read book Stochastic Dynamics for Systems Biology written by Christian Mazza and published by CRC Press. This book was released on 2016-04-19 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Dynamics for Systems Biology is one of the first books to provide a systematic study of the many stochastic models used in systems biology. The book shows how the mathematical models are used as technical tools for simulating biological processes and how the models lead to conceptual insights on the functioning of the cellular processing

Discrete-time Stochastic Systems

Author : Torsten Söderström
Publisher : Springer Science & Business Media
ISBN 13 : 9781852336493
Total Pages : 410 pages
Book Rating : 4.3/5 (364 download)

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Book Synopsis Discrete-time Stochastic Systems by : Torsten Söderström

Download or read book Discrete-time Stochastic Systems written by Torsten Söderström and published by Springer Science & Business Media. This book was released on 2002-07-26 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive introduction to the estimation and control of dynamic stochastic systems provides complete derivations of key results. The second edition includes improved and updated material, and a new presentation of polynomial control and new derivation of linear-quadratic-Gaussian control.

Stochastic Dynamics in Computational Biology

Author : Stefanie Winkelmann
Publisher : Springer Nature
ISBN 13 : 3030623874
Total Pages : 284 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Stochastic Dynamics in Computational Biology by : Stefanie Winkelmann

Download or read book Stochastic Dynamics in Computational Biology written by Stefanie Winkelmann and published by Springer Nature. This book was released on 2021-01-04 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to provide a well-structured and coherent overview of existing mathematical modeling approaches for biochemical reaction systems, investigating relations between both the conventional models and several types of deterministic-stochastic hybrid model recombinations. Another main objective is to illustrate and compare diverse numerical simulation schemes and their computational effort. Unlike related works, this book presents a broad scope in its applications, from offering a detailed introduction to hybrid approaches for the case of multiple population scales to discussing the setting of time-scale separation resulting from widely varying firing rates of reaction channels. Additionally, it also addresses modeling approaches for non well-mixed reaction-diffusion dynamics, including deterministic and stochastic PDEs and spatiotemporal master equations. Finally, by translating and incorporating complex theory to a level accessible to non-mathematicians, this book effectively bridges the gap between mathematical research in computational biology and its practical use in biological, biochemical, and biomedical systems.

Stochastic Dynamics Of Complex Systems: From Glasses To Evolution

Author : Henrik Jeldtoft Jensen
Publisher : World Scientific Publishing Company
ISBN 13 : 1848169957
Total Pages : 300 pages
Book Rating : 4.8/5 (481 download)

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Book Synopsis Stochastic Dynamics Of Complex Systems: From Glasses To Evolution by : Henrik Jeldtoft Jensen

Download or read book Stochastic Dynamics Of Complex Systems: From Glasses To Evolution written by Henrik Jeldtoft Jensen and published by World Scientific Publishing Company. This book was released on 2013-02-20 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamical evolution over long time scales is a prominent feature of all the systems we intuitively think of as complex — for example, ecosystems, the brain or the economy. In physics, the term ageing is used for this type of slow change, occurring over time scales much longer than the patience, or indeed the lifetime, of the observer. The main focus of this book is on the stochastic processes which cause ageing, and the surprising fact that the ageing dynamics of systems which are very different at the microscopic level can be treated in similar ways.The first part of this book provides the necessary mathematical and computational tools and the second part describes the intuition needed to deal with these systems. Some of the first few chapters have been covered in several other books, but the emphasis and selection of the topics reflect both the authors' interests and the overall theme of the book. The second part contains an introduction to the scientific literature and deals in some detail with the description of complex phenomena of a physical and biological nature, for example, disordered magnetic materials, superconductors and glasses, models of co-evolution in ecosystems and even of ant behaviour. These heterogeneous topics are all dealt with in detail using similar analytical techniques.This book emphasizes the unity of complex dynamics and provides the tools needed to treat a large number of complex systems of current interest. The ideas and the approach to complex dynamics it presents have not appeared in book form until now./a

Recent Development In Stochastic Dynamics And Stochastic Analysis

Author : Jinqiao Duan
Publisher : World Scientific
ISBN 13 : 981446760X
Total Pages : 306 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Recent Development In Stochastic Dynamics And Stochastic Analysis by : Jinqiao Duan

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 2010-02-08 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 to 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.

Analysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems

Author : M. Reza Rahimi Tabar
Publisher : Springer
ISBN 13 : 3030184722
Total Pages : 280 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Analysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems by : M. Reza Rahimi Tabar

Download or read book Analysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems written by M. Reza Rahimi Tabar and published by Springer. This book was released on 2019-07-04 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.

Nonlinear and Stochastic Climate Dynamics

Author : Christian L. E. Franzke
Publisher : Cambridge University Press
ISBN 13 : 1316883213
Total Pages : 612 pages
Book Rating : 4.3/5 (168 download)

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Book Synopsis Nonlinear and Stochastic Climate Dynamics by : Christian L. E. Franzke

Download or read book Nonlinear and Stochastic Climate Dynamics written by Christian L. E. Franzke and published by Cambridge University Press. This book was released on 2017-01-19 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is now widely recognized that the climate system is governed by nonlinear, multi-scale processes, whereby memory effects and stochastic forcing by fast processes, such as weather and convective systems, can induce regime behavior. Motivated by present difficulties in understanding the climate system and to aid the improvement of numerical weather and climate models, this book gathers contributions from mathematics, physics and climate science to highlight the latest developments and current research questions in nonlinear and stochastic climate dynamics. Leading researchers discuss some of the most challenging and exciting areas of research in the mathematical geosciences, such as the theory of tipping points and of extreme events including spatial extremes, climate networks, data assimilation and dynamical systems. This book provides graduate students and researchers with a broad overview of the physical climate system and introduces powerful data analysis and modeling methods for climate scientists and applied mathematicians.