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Author : Anatoli V Skorokhod,Frank C Hoppensteadt,Habib D Salehi
Publisher : Unknown
Page : 504 pages
File Size : 55,9 Mb
Release : 2002-07-09
Category : Electronic
ISBN : 1468492705
Author : Anatoli V. Skorokhod,Frank C. Hoppensteadt,Habib D. Salehi
Publisher : Springer Science & Business Media
Page : 498 pages
File Size : 47,8 Mb
Release : 2007-06-21
Category : Mathematics
ISBN : 9780387224466
This book develops methods for describing random dynamical systems, and it illustrats how the methods can be used in a variety of applications. Appeals to researchers and graduate students who require tools to investigate stochastic systems.
Author : Anatoli V. Skorokhod,Frank C. Hoppensteadt,Habib D. Salehi
Publisher : Springer Science & Business Media
Page : 500 pages
File Size : 44,9 Mb
Release : 2007-06-21
Category : Mathematics
ISBN : 9780387224466
This book develops methods for describing random dynamical systems, and it illustrats how the methods can be used in a variety of applications. Appeals to researchers and graduate students who require tools to investigate stochastic systems.
Author : İlkay Bakırtaş
Publisher : BoD – Books on Demand
Page : 170 pages
File Size : 44,9 Mb
Release : 2018-10-17
Category : Mathematics
ISBN : 9781789842555
The governing equations of mathematical, chemical, biological, mechanical and economical models are often nonlinear and too complex to be solved analytically. Perturbation theory provides effective tools for obtaining approximate analytical solutions to a wide variety of such nonlinear problems, which may include differential or difference equations. In this book, we aim to present the recent developments and applications of the perturbation theory for treating problems in applied mathematics, physics and engineering. The eight chapters cover a variety of topics related to perturbation methods. The book is intended to draw attention of researchers and scientist in academia and industry.
Author : İlkay Bakırtaş
Publisher : Unknown
Page : 168 pages
File Size : 47,6 Mb
Release : 2018
Category : Mathematics
ISBN : 1789842565
The governing equations of mathematical, chemical, biological, mechanical and economical models are often nonlinear and too complex to be solved analytically. Perturbation theory provides effective tools for obtaining approximate analytical solutions to a wide variety of such nonlinear problems, which may include differential or difference equations. In this book, we aim to present the recent developments and applications of the perturbation theory for treating problems in applied mathematics, physics and engineering. The eight chapters cover a variety of topics related to perturbation methods. The book is intended to draw attention of researchers and scientist in academia and industry.
Author : Anatoliy M Samoilenko,Oleksandr Stanzhytskyi
Publisher : World Scientific
Page : 324 pages
File Size : 45,5 Mb
Release : 2011-06-07
Category : Mathematics
ISBN : 9789814462396
Differential equations with random perturbations are the mathematical models of real-world processes that cannot be described via deterministic laws, and their evolution depends on random factors. The modern theory of differential equations with random perturbations is on the edge of two mathematical disciplines: random processes and ordinary differential equations. Consequently, the sources of these methods come both from the theory of random processes and from the classic theory of differential equations. This work focuses on the approach to stochastic equations from the perspective of ordinary differential equations. For this purpose, both asymptotic and qualitative methods which appeared in the classical theory of differential equations and nonlinear mechanics are developed. Contents:Differential Equations with Random Right-Hand Sides and Impulsive EffectsInvariant Sets for Systems with Random PerturbationsLinear and Quasilinear Stochastic Ito SystemsExtensions of Ito Systems on a TorusThe Averaging Method for Equations with Random Perturbations Readership: Graduate students and researchers in mathematics and physics. Keywords:Stochastic Systems;Invariant Manifold;Invariant Torus;Lyapunov Function;Stability;Periodic Solutions;Reduction PrincipleKey Features:Develops new methods of studying the stochastic differential equations; contrary to the existing purely probabilistic methods, these methods are based on the differential equations approachStudies new classes of stochastic systems, for instance, the stochastic expansions of dynamical systems on the torus, enabling the study of general oscillatory systems subject to the influences of random factorsBridges the gap between the stochastic differential equations and ordinary differential equations, namely, it describes which properties of the ordinary differential equations remain unchanged, and which new properties appear in the stochastic caseReviews: "This book is well written and readable. Most results included in the book are by the authors. All chapters contain a final section with comments and references, where the authors make a detailed description of the origin of the results. This is a helpful point for all readers, especially for researchers in the field." Mathematical Reviews "This monograph collects a great variety of stimulating results concerning random perturbation theory always deeply rooted in the classical theory of ordinary differential equations and celestial mechanics. Despite its technical content the text is written in a clear and accessible way, with many insightful explanations. The fact that each chapter closes with a detailed review on the current literature and the historic development of the theory is highly appreciated." Zentralblatt MATH
Author : Nikolaos Limnios,Anatoliy Swishchuk
Publisher : Springer Nature
Page : 206 pages
File Size : 53,7 Mb
Release : 2023-07-24
Category : Mathematics
ISBN : 9783031334290
This book extends the theory and applications of random evolutions to semi-Markov random media in discrete time, essentially focusing on semi-Markov chains as switching or driving processes. After giving the definitions of discrete-time semi-Markov chains and random evolutions, it presents the asymptotic theory in a functional setting, including weak convergence results in the series scheme, and their extensions in some additional directions, including reduced random media, controlled processes, and optimal stopping. Finally, applications of discrete-time semi-Markov random evolutions in epidemiology and financial mathematics are discussed. This book will be of interest to researchers and graduate students in applied mathematics and statistics, and other disciplines, including engineering, epidemiology, finance and economics, who are concerned with stochastic models of systems.
Author : Yu. Kabanov,R. Liptser,J. Stoyanov
Publisher : Springer Science & Business Media
Page : 633 pages
File Size : 54,7 Mb
Release : 2007-04-03
Category : Mathematics
ISBN : 9783540307884
Dedicated to the Russian mathematician Albert Shiryaev on his 70th birthday, this is a collection of papers written by his former students, co-authors and colleagues. The book represents the modern state of art of a quickly maturing theory and will be an essential source and reading for researchers in this area. Diversity of topics and comprehensive style of the papers make the book attractive for PhD students and young researchers.
Author : Jie Li,Jianbing Chen
Publisher : John Wiley & Sons
Page : 426 pages
File Size : 54,6 Mb
Release : 2009-07-23
Category : Technology & Engineering
ISBN : 9780470824252
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
Author : Dmitri Koroliouk,Igor Samoilenko
Publisher : John Wiley & Sons
Page : 345 pages
File Size : 55,9 Mb
Release : 2021-08-02
Category : Mathematics
ISBN : 9781119851240
Within the field of modeling complex objects in natural sciences, which considers systems that consist of a large number of interacting parts, a good tool for analyzing and fitting models is the theory of random evolutionary systems, considering their asymptotic properties and large deviations. In Random Evolutionary Systems we consider these systems in terms of the operators that appear in the schemes of their diffusion and the Poisson approximation. Such an approach allows us to obtain a number of limit theorems and asymptotic expansions of processes that model complex stochastic systems, both those that are autonomous and those dependent on an external random environment. In this case, various possibilities of scaling processes and their time parameters are used to obtain different limit results.
Author : Frank Charles Hoppensteadt
Publisher : American Mathematical Soc.
Page : 182 pages
File Size : 41,5 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821852699
Based on a course on advanced topics in differential equations given at the Courant Institute of Mathematical Sciences, this book describes aspects of mathematical modeling, analysis, computer simulation, and visualization in the mathematical sciences and engineering that involve singular perturbations.
Author : brian straughan
Publisher : Springer Science & Business Media
Page : 470 pages
File Size : 40,5 Mb
Release : 2003-10-01
Category : Mathematics
ISBN : 038700453X
Six new chapters (14-19) deal with topics of current interest: multi-component convection diffusion, convection in a compressible fluid, convenction with temperature dependent viscosity and thermal conductivity, penetrative convection, nonlinear stability in ocean circulation models, and numerical solution of eigenvalue problems.
Author : V.V. Rykov,N. Balakrishnan,M.S. Nikulin
Publisher : Springer Science & Business Media
Page : 465 pages
File Size : 48,8 Mb
Release : 2010-11-02
Category : Technology & Engineering
ISBN : 9780817649715
The book is a selection of invited chapters, all of which deal with various aspects of mathematical and statistical models and methods in reliability. Written by renowned experts in the field of reliability, the contributions cover a wide range of applications, reflecting recent developments in areas such as survival analysis, aging, lifetime data analysis, artificial intelligence, medicine, carcinogenesis studies, nuclear power, financial modeling, aircraft engineering, quality control, and transportation. Mathematical and Statistical Models and Methods in Reliability is an excellent reference text for researchers and practitioners in applied probability and statistics, industrial statistics, engineering, medicine, finance, transportation, the oil and gas industry, and artificial intelligence.
Author : Hansjörg Kielhöfer
Publisher : Springer Science & Business Media
Page : 355 pages
File Size : 43,6 Mb
Release : 2006-04-10
Category : Mathematics
ISBN : 9780387216331
In the past three decades, bifurcation theory has matured into a well-established and vibrant branch of mathematics. This book gives a unified presentation in an abstract setting of the main theorems in bifurcation theory, as well as more recent and lesser known results. It covers both the local and global theory of one-parameter bifurcations for operators acting in infinite-dimensional Banach spaces, and shows how to apply the theory to problems involving partial differential equations. In addition to existence, qualitative properties such as stability and nodal structure of bifurcating solutions are treated in depth. This volume will serve as an important reference for mathematicians, physicists, and theoretically-inclined engineers working in bifurcation theory and its applications to partial differential equations.
Author : Kiyohiro Ikeda,Kazuo Murota
Publisher : Springer Science & Business Media
Page : 426 pages
File Size : 40,8 Mb
Release : 2013-03-09
Category : Science
ISBN : 9781475736977
Most physical systems lose or gain stability through bifurcation behavior. This book explains a series of experimentally found bifurcation phenomena by means of the methods of static bifurcation theory.
