Dynamics Of Quasi Stable Dissipative Systems
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Dynamics Of Quasi Stable Dissipative Systems
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Author : Igor Chueshov
language : en
Publisher: Springer
Release Date : 2015-09-29
Dynamics Of Quasi Stable Dissipative Systems written by Igor Chueshov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-29 with Mathematics categories.
This book is devoted to background material and recently developed mathematical methods in the study of infinite-dimensional dissipative systems. The theory of such systems is motivated by the long-term goal to establish rigorous mathematical models for turbulent and chaotic phenomena. The aim here is to offer general methods and abstract results pertaining to fundamental dynamical systems properties related to dissipative long-time behavior. The book systematically presents, develops and uses the quasi-stability method while substantially extending it by including for consideration new classes of models and PDE systems arising in Continuum Mechanics. The book can be used as a textbook in dissipative dynamics at the graduate level. Igor Chueshov is a Professor of Mathematics at Karazin Kharkov National University in Kharkov, Ukraine.
Structures In Dynamics
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Author : H.W. Broer
language : en
Publisher: Elsevier
Release Date : 1991-11-05
Structures In Dynamics written by H.W. Broer and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-11-05 with Science categories.
The study of non-linear dynamical systems nowadays is an intricate mixture of analysis, geometry, algebra and measure theory and this book takes all aspects into account. Presenting the contents of its authors' graduate courses in non-linear dynamical systems, this volume aims at researchers who wish to be acquainted with the more theoretical and fundamental subjects in non-linear dynamics and is designed to link the popular literature with research papers and monographs. All of the subjects covered in this book are extensively dealt with and presented in a pedagogic form. These include the presentation of an environment for the route to chaos by quasi-periodicity (which is related to the Landau-Lifschitz and Ruelle-Takens scenario's concerning the onset of turbulence); the theories of 1-dimensional dynamics, singularities in planar vector fields, and quasi-periodicity in dissipative systems.
Elementary Symbolic Dynamics And Chaos In Dissipative Systems
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Author : Hao Bailin
language : en
Publisher: World Scientific
Release Date : 1989-09-01
Elementary Symbolic Dynamics And Chaos In Dissipative Systems written by Hao Bailin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-09-01 with Science categories.
This book is a monograph on chaos in dissipative systems written for those working in the physical sciences. Emphasis is on symbolic description of the dynamics and various characteristics of the attractors, and written from the view-point of practical applications without going into formal mathematical rigour. The author used elementary mathematics and calculus, and relied on physical intuition whenever possible. Substantial attention is paid to numerical techniques in the study of chaos. Part of the book is based on the publications of Chinese researchers, including those of the author's collaborators. Contents:Mathematical Models Exhibiting ChaosOne Dimensional MappingsElementary Symbolic DynamicsCircle Mappings and Two-Dimensional MapsChaos in Ordinary Differential EquationsCharacterization of Chaotic AttractorsTransient Behaviour Readership: Condensed matter physicists, applied mathematicians and computer scientists. Keywords:Symbolic Dynamics;One Dimensional Mappings;Circle Mapping;Two-Dimensional Maps;Chaotic Attractors;Transient Behaviour
Dissipative Lattice Dynamical Systems
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Author : Xiaoying Han
language : en
Publisher: World Scientific
Release Date : 2023-03-14
Dissipative Lattice Dynamical Systems written by Xiaoying Han and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-14 with Mathematics categories.
There is an extensive literature in the form of papers (but no books) on lattice dynamical systems. The book focuses on dissipative lattice dynamical systems and their attractors of various forms such as autonomous, nonautonomous and random. The existence of such attractors is established by showing that the corresponding dynamical system has an appropriate kind of absorbing set and is asymptotically compact in some way.There is now a very large literature on lattice dynamical systems, especially on attractors of all kinds in such systems. We cannot hope to do justice to all of them here. Instead, we have focused on key areas of representative types of lattice systems and various types of attractors. Our selection is biased by our own interests, in particular to those dealing with biological applications. One of the important results is the approximation of Heaviside switching functions in LDS by sigmoidal functions.Nevertheless, we believe that this book will provide the reader with a solid introduction to the field, its main results and the methods that are used to obtain them.
Stability And Control Of Large Scale Dynamical Systems
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Author : Wassim M. Haddad
language : en
Publisher: Princeton University Press
Release Date : 2011-12-04
Stability And Control Of Large Scale Dynamical Systems written by Wassim M. Haddad 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 2011-12-04 with Mathematics categories.
Modern complex large-scale dynamical systems exist in virtually every aspect of science and engineering, and are associated with a wide variety of technological, environmental, and social phenomena. This book develops stability analysis and control design framework for nonlinear large-scale interconnected dynamical systems.
Impulsive And Hybrid Dynamical Systems
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Author : Wassim M. Haddad
language : en
Publisher: Princeton University Press
Release Date : 2006-07-23
Impulsive And Hybrid Dynamical Systems written by Wassim M. Haddad 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 2006-07-23 with Mathematics categories.
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Contemporary Approaches And Methods In Fundamental Mathematics And Mechanics
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Author : Victor A. Sadovnichiy
language : en
Publisher: Springer Nature
Release Date : 2020-11-24
Contemporary Approaches And Methods In Fundamental Mathematics And Mechanics written by Victor A. Sadovnichiy and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-24 with Mathematics categories.
This book focuses on the latest approaches and methods in fundamental mathematics and mechanics, and discusses the practical application of abstract mathematical approaches, such as differential geometry, and differential and difference equations in solid mechanics, hydrodynamics, aerodynamics, optimization, decision-making theory and control theory. Featuring selected contributions to the open seminar series of Lomonosov Moscow State University and Igor Sikorsky Kyiv Polytechnic Institute by mathematicians from China, Germany, France, Italy, Spain, Russia, Ukraine and the USA, the book will appeal to mathematicians and engineers working at the interface of these fields
Dynamics Of Asymmetric Dissipative Systems
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Author : Yuki Sugiyama
language : en
Publisher: Springer Nature
Release Date : 2023-11-15
Dynamics Of Asymmetric Dissipative Systems written by Yuki Sugiyama and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-15 with Mathematics categories.
This book provides the dynamics of non-equilibrium dissipative systems with asymmetric interactions (Asymmetric Dissipative System; ADS). Asymmetric interaction breaks "the law of action and reaction" in mechanics, and results in non-conservation of the total momentum and energy. In such many-particle systems, the inflow of energy is provided and the energy flows out as dissipation. The emergences of non-trivial macroscopic phenomena occur in the non-equilibrium energy balance owing to the effect of collective motions as phase transitions and bifurcations. ADS are applied to the systems of self-driven interacting particles such as traffic and granular flows, pedestrians and evacuations, and collective movement of living systems. The fundamental aspects of dynamics in ADS are completely presented by a minimal mathematical model, the Optimal Velocity (OV) Model. Using that model, the basics of mathematical and physical mechanisms of ADS are described analytically with exact results. The application of 1-dimensional motions is presented for traffic jam formation. The mathematical theory is compared with empirical data of experiments and observations on highways. In 2-dimensional motion pattern formations of granular media, pedestrians, and group formations of organisms are described. The common characteristics of emerged moving objects are a variety of patterns, flexible deformations, and rapid response against stimulus. Self-organization and adaptation in group formations and control of group motions are shown in examples. Another OV Model formulated by a delay differential equation is provided with exact solutions using elliptic functions. The relations to soliton systems are described. Moreover, several topics in ADS are presented such as the similarity between the spatiotemporal patterns, violation of fluctuation dissipation relation, and a thermodynamic function for governing the phase transition in non-equilibrium stationary states.
Bifurcation And Stability Of Dissipative Systems
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Author : International Centre for Mechanical Sciences
language : en
Publisher: Springer
Release Date : 1993
Bifurcation And Stability Of Dissipative Systems written by International Centre for Mechanical Sciences and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Science categories.
Quantum Dissipative Systems Fifth Edition
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Author : Ulrich Weiss
language : en
Publisher: World Scientific
Release Date : 2021-09-21
Quantum Dissipative Systems Fifth Edition written by Ulrich Weiss and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-21 with Science categories.
This comprehensive textbook provides the fundamental concepts and methods of dissipative quantum mechanics and related issues in condensed matter physics starting from first principles. It deals with the phenomena and theory of decoherence, relaxation and dissipation in quantum mechanics that arise from the random exchange of energy with the environment. Major theoretical advances in combination with stunning experimental achievements and the arising perspective for quantum computing have brightened the field and brought it to the attention of the general community in natural sciences. Expertise in dissipative quantum mechanics is by now beneficial in a broad sphere.This book — originally published in 1992 and republished as enlarged and updated second, third and fourth edition in 1999, 2008, and 2012 — dives even deeper into the fundamental concepts, methods and applications of quantum dissipation. The fifth edition provides a self-contained and updated account of the quantum mechanics and quantum statistics of open systems. The subject matter of the book has been thoroughly revised to better comply with the needs of newcomers and the demands of the advanced readership. Most of the chapters are rewritten to enhance clarity and topicality. Four new chapters covering recent developments in the field have been added. There are about 600 references. This book is intended for use by advanced undergraduate and graduate students in physics, and for researchers active in the field. They will find the monograph as a rich and stimulating source.