Stochastic Dynamical Systems
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Stochastic Dynamical Systems
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Author : Josef Honerkamp
language : de
Publisher: John Wiley & Sons
Release Date : 1996-12-17
Stochastic Dynamical Systems written by Josef Honerkamp and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-12-17 with Mathematics categories.
Dieser einzigartige Band führt den Leser in die mathematische Begriffsbildung für komplexe Systeme ein. Er ist ideal für Studenten der Mathematik, Physik, Chemie und Medizin, die sich in ihrem Studium erstmals mit stochastischen dynamischen Systemen beschäftigen. Das Buch stellt praktische Methoden zur Verfügung, um mit solchen Systemen umgehen zu können, und stellt die zugundeliegenden Definitionen und theoretischen Annahmen, wo erforderlich, klar heraus. Im Gegensatz zu anderen Büchern über dieses Gebiet, die oft einen bestimmten Zugang bevorzugen, deckt Stochastical Dynamical Systems eine Vielzahl von stochastischen und statistischen Methoden ab, die für die Untersuchung von komplexen Systemen wie Polymerschmelzen, dem menschlichen Körper und der Atmosphäre absolut notwendig sind. Das Buch behandelt die Datenanalyse ebenso wie Simulationsmethoden für gegebene Modelle. Die ganze Vielfalt der klassischen und neuartigen Begriffe der mathematischen Stochastik wird in einem leicht verständlichen Stil erklärt, so daß die Leser diese Konzepte leicht für die Untersuchung ihrer Daten anwenden können.
Chaotic Transitions In Deterministic And Stochastic Dynamical Systems
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Author : Emil Simiu
language : en
Publisher: Princeton University Press
Release Date : 2009-06-28
Chaotic Transitions In Deterministic And Stochastic Dynamical Systems written by Emil Simiu and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-28 with Mathematics categories.
The classical Melnikov method provides information on the behavior of deterministic planar systems that may exhibit transitions, i.e. escapes from and captures into preferred regions of phase space. This book develops a unified treatment of deterministic and stochastic systems that extends the applicability of the Melnikov method to physically realizable stochastic planar systems with additive, state-dependent, white, colored, or dichotomous noise. The extended Melnikov method yields the novel result that motions with transitions are chaotic regardless of whether the excitation is deterministic or stochastic. It explains the role in the occurrence of transitions of the characteristics of the system and its deterministic or stochastic excitation, and is a powerful modeling and identification tool. The book is designed primarily for readers interested in applications. The level of preparation required corresponds to the equivalent of a first-year graduate course in applied mathematics. No previous exposure to dynamical systems theory or the theory of stochastic processes is required. The theoretical prerequisites and developments are presented in the first part of the book. The second part of the book is devoted to applications, ranging from physics to mechanical engineering, naval architecture, oceanography, nonlinear control, stochastic resonance, and neurophysiology.
Random Dynamical Systems
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Author : Ludwig Arnold
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Random Dynamical Systems written by Ludwig Arnold 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 2013-04-17 with Mathematics categories.
Background and Scope of the Book This book continues, extends, and unites various developments in the intersection of probability theory and dynamical systems. I will briefly outline the background of the book, thus placing it in a systematic and historical context and tradition. Roughly speaking, a random dynamical system is a combination of a measure-preserving dynamical system in the sense of ergodic theory, (D,F,lP', (B(t))tE'lf), 'II'= JR+, IR, z+, Z, with a smooth (or topological) dy namical system, typically generated by a differential or difference equation :i: = f(x) or Xn+l = tp(x.,), to a random differential equation :i: = f(B(t)w,x) or random difference equation Xn+l = tp(B(n)w, Xn)· Both components have been very well investigated separately. However, a symbiosis of them leads to a new research program which has only partly been carried out. As we will see, it also leads to new problems which do not emerge if one only looks at ergodic theory and smooth or topological dynam ics separately. From a dynamical systems point of view this book just deals with those dynamical systems that have a measure-preserving dynamical system as a factor (or, the other way around, are extensions of such a factor). As there is an invariant measure on the factor, ergodic theory is always involved.
Dynamics Of Stochastic Systems
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Author : Valery I. Klyatskin
language : en
Publisher: Elsevier
Release Date : 2005-03-17
Dynamics Of Stochastic Systems written by Valery I. Klyatskin and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-03-17 with Science categories.
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
Handbook Of Dynamics And Probability
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Author : Peter Müller
language : en
Publisher: Springer Nature
Release Date : 2021-11-20
Handbook Of Dynamics And Probability written by Peter Müller and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-20 with Science categories.
Our time is characterized by an explosive growth in the use of ever more complicated and sophisticated (computer) models. These models rely on dynamical systems theory for the interpretation of their results and on probability theory for the quantification of their uncertainties. A conscientious and intelligent use of these models requires that both these theories are properly understood. This book is to provide such understanding. It gives a unifying treatment of dynamical systems theory and probability theory. It covers the basic concepts and statements of these theories, their interrelations, and their applications to scientific reasoning and physics. The book stresses the underlying concepts and mathematical structures but is written in a simple and illuminating manner without sacrificing too much mathematical rigor. The book is aimed at students, post-docs, and researchers in the applied sciences who aspire to better understand the conceptual and mathematical underpinnings of the models that they use. Despite the peculiarities of any applied science, dynamics and probability are the common and indispensable tools in any modeling effort. The book is self-contained, with many technical aspects covered in appendices, but does require some basic knowledge in analysis, linear algebra, and physics. Peter Müller, now a professor emeritus at the University of Hawaii, has worked extensively on ocean and climate models and the foundations of complex system theories.
Stochastic Dynamics For Systems Biology
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Author : Christian Mazza
language : en
Publisher: CRC Press
Release Date : 2016-04-19
Stochastic Dynamics For Systems Biology written by Christian Mazza and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Mathematics categories.
This 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 system. Examples cover the phage lambda genetic switch, eukaryotic gene expression, noise propagation in gene networks, and more. Most of the text should be accessible to scientists with basic knowledge in calculus and probability theory.
Stochastic Approximation
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Author : Vivek S. Borkar
language : en
Publisher: Springer
Release Date : 2009-01-01
Stochastic Approximation written by Vivek S. Borkar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-01 with Mathematics categories.
The Fokker Planck Equation For Stochastic Dynamical Systems And Its Explicit Steady State Solutions
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Author : Christian Soize
language : en
Publisher: World Scientific
Release Date : 1994
The Fokker Planck Equation For Stochastic Dynamical Systems And Its Explicit Steady State Solutions written by Christian Soize and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Science categories.
This is an analysis of multidimensional nonlinear dissipative Hamiltonian dynamical systems subjected to parametric and external stochastic excitations by the Fokker-Planck equation method.The author answers three types of questions concerning this area. First, what probabilistic tools are necessary for constructing a stochastic model and deriving the FKP equation for nonlinear stochastic dynamical systems? Secondly, what are the main results concerning the existence and uniqueness of an invariant measure and its associated stationary response? Finally, what is the class of multidimensional dynamical systems that have an explicit invariant measure and what are the fundamental examples for applications?
Linearization Methods For Stochastic Dynamic Systems
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Author : Leslaw Socha
language : en
Publisher: Springer
Release Date : 2007-11-30
Linearization Methods For Stochastic Dynamic Systems written by Leslaw Socha and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-30 with Technology & Engineering categories.
For most cases of interest, exact solutions to nonlinear equations describing stochastic dynamical systems are not available. This book details the relatively simple and popular linearization techniques available, covering theory as well as application. It examines models with continuous external and parametric excitations, those that cover the majority of known approaches.