Dynamics Of Quasi Stable Dissipative Systems

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Dynamics of Quasi-Stable Dissipative Systems

Author : Igor Chueshov
Publisher : Springer
ISBN 13 : 3319229036
Total Pages : 405 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Dynamics of Quasi-Stable Dissipative Systems by : Igor Chueshov

Download or read book Dynamics of Quasi-Stable Dissipative Systems written by Igor Chueshov and published by Springer. This book was released on 2015-09-29 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Stability and Control of Large-Scale Dynamical Systems

Author : Wassim M. Haddad
Publisher : Princeton University Press
ISBN 13 : 1400842662
Total Pages : 389 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Stability and Control of Large-Scale Dynamical Systems by : Wassim M. Haddad

Download or read book Stability and Control of Large-Scale Dynamical Systems written by Wassim M. Haddad and published by Princeton University Press. This book was released on 2011-11-14 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern complex large-scale dynamical systems exist in virtually every aspect of science and engineering, and are associated with a wide variety of physical, technological, environmental, and social phenomena, including aerospace, power, communications, and network systems, to name just a few. This book develops a general stability analysis and control design framework for nonlinear large-scale interconnected dynamical systems, and presents the most complete treatment on vector Lyapunov function methods, vector dissipativity theory, and decentralized control architectures. Large-scale dynamical systems are strongly interconnected and consist of interacting subsystems exchanging matter, energy, or information with the environment. The sheer size, or dimensionality, of these systems necessitates decentralized analysis and control system synthesis methods for their analysis and design. Written in a theorem-proof format with examples to illustrate new concepts, this book addresses continuous-time, discrete-time, and hybrid large-scale systems. It develops finite-time stability and finite-time decentralized stabilization, thermodynamic modeling, maximum entropy control, and energy-based decentralized control. This book will interest applied mathematicians, dynamical systems theorists, control theorists, and engineers, and anyone seeking a fundamental and comprehensive understanding of large-scale interconnected dynamical systems and control.

Dissipative Lattice Dynamical Systems

Author : Xiaoying Han
Publisher : World Scientific
ISBN 13 : 9811267774
Total Pages : 381 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Dissipative Lattice Dynamical Systems by : Xiaoying Han

Download or read book Dissipative Lattice Dynamical Systems written by Xiaoying Han and published by World Scientific. This book was released on 2023-03-14 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Structures in Dynamics

Author : H.W. Broer
Publisher : Elsevier
ISBN 13 : 0444596259
Total Pages : 323 pages
Book Rating : 4.4/5 (445 download)

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Book Synopsis Structures in Dynamics by : H.W. Broer

Download or read book Structures in Dynamics written by H.W. Broer and published by Elsevier. This book was released on 1991-11-05 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to the Theory of Infinite-dimensional Dissipative Systems

Author : Igor' D. Čuešov
Publisher : "Acta" publishers
ISBN 13 : 9667021645
Total Pages : 421 pages
Book Rating : 4.6/5 (67 download)

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Book Synopsis Introduction to the Theory of Infinite-dimensional Dissipative Systems by : Igor' D. Čuešov

Download or read book Introduction to the Theory of Infinite-dimensional Dissipative Systems written by Igor' D. Čuešov and published by "Acta" publishers. This book was released on 2002 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Patterns and Interfaces in Dissipative Dynamics

Author : L.M. Pismen
Publisher : Springer Science & Business Media
ISBN 13 : 3540304312
Total Pages : 383 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Patterns and Interfaces in Dissipative Dynamics by : L.M. Pismen

Download or read book Patterns and Interfaces in Dissipative Dynamics written by L.M. Pismen and published by Springer Science & Business Media. This book was released on 2006-07-07 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spontaneous pattern formation in nonlinear dissipative systems far from equilibrium occurs in a variety of settings in nature and technology, and has applications ranging from nonlinear optics through solid and fluid mechanics, physical chemistry and chemical engineering to biology. This book explores the forefront of current research, describing in-depth the analytical methods that elucidate the complex evolution of nonlinear dissipative systems.

Elementary Symbolic Dynamics and Chaos in Dissipative Systems

Author : Bai-Lin Hao
Publisher : World Scientific
ISBN 13 : 9789971506988
Total Pages : 488 pages
Book Rating : 4.5/5 (69 download)

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Book Synopsis Elementary Symbolic Dynamics and Chaos in Dissipative Systems by : Bai-Lin Hao

Download or read book Elementary Symbolic Dynamics and Chaos in Dissipative Systems written by Bai-Lin Hao and published by World Scientific. This book was released on 1989 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Dissipative Systems Analysis and Control

Author : Rogelio Lozano
Publisher : Springer Science & Business Media
ISBN 13 : 1447136683
Total Pages : 383 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Dissipative Systems Analysis and Control by : Rogelio Lozano

Download or read book Dissipative Systems Analysis and Control written by Rogelio Lozano and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the analysis and feedback control of dissipative dynamical systems. It presents the background of dissipative systems theory. Linear as well as nonlinear systems are treated, and many examples are given throughout the chapters. Some infinite dimensional and non-smooth examples are also included. The emphasis is put on the application towards the design of stable feedback control laws. Then the theory is illustrated on physical examples; (Lagrangian and Hamiltonian systems are thoroughly studied, as well as adaptive control). It is shown how the dissipativity properties of a system can be used in the design of stable feedback controllers. Some experimental results are presented which corroborate the theoretical developments. This monograph is primarily for readers who wish to get aquainted with Dissipative Systems Theory, and its uses in Systems and Control and Robotics. It constitutes an advanced introduction to the topic, and is the first volume ever published which is dedicated entirely to this subject.

Contemporary Approaches and Methods in Fundamental Mathematics and Mechanics

Author : Victor A. Sadovnichiy
Publisher : Springer Nature
ISBN 13 : 303050302X
Total Pages : 525 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Contemporary Approaches and Methods in Fundamental Mathematics and Mechanics by : Victor A. Sadovnichiy

Download or read book Contemporary Approaches and Methods in Fundamental Mathematics and Mechanics written by Victor A. Sadovnichiy and published by Springer Nature. This book was released on 2020-11-24 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Attractors for Semigroups and Evolution Equations

Author : Olga A. Ladyzhenskaya
Publisher : Cambridge University Press
ISBN 13 : 1009229796
Total Pages : pages
Book Rating : 4.0/5 (92 download)

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Book Synopsis Attractors for Semigroups and Evolution Equations by : Olga A. Ladyzhenskaya

Download or read book Attractors for Semigroups and Evolution Equations written by Olga A. Ladyzhenskaya and published by Cambridge University Press. This book was released on 2022-06-09 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, Olga A. Ladyzhenskaya expands on her highly successful 1991 Accademia Nazionale dei Lincei lectures. The lectures were devoted to questions of the behaviour of trajectories for semigroups of nonlinear bounded continuous operators in a locally non-compact metric space and for solutions of abstract evolution equations. The latter contain many initial boundary value problems for dissipative partial differential equations. This work, for which Ladyzhenskaya was awarded the Russian Academy of Sciences' Kovalevskaya Prize, reflects the high calibre of her lectures; it is essential reading for anyone interested in her approach to partial differential equations and dynamical systems. This edition, reissued for her centenary, includes a new technical introduction, written by Gregory A. Seregin, Varga K. Kalantarov and Sergey V. Zelik, surveying Ladyzhenskaya's works in the field and subsequent developments influenced by her results.

Dynamics of Asymmetric Dissipative Systems

Author : Yuki Sugiyama
Publisher : Springer Nature
ISBN 13 : 9819918707
Total Pages : 322 pages
Book Rating : 4.8/5 (199 download)

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Book Synopsis Dynamics of Asymmetric Dissipative Systems by : Yuki Sugiyama

Download or read book Dynamics of Asymmetric Dissipative Systems written by Yuki Sugiyama and published by Springer Nature. This book was released on 2023-11-15 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Stability of Quasi-linear Hyperbolic Dissipative Systems

Author : Heinz Kreiss
Publisher :
ISBN 13 :
Total Pages : 23 pages
Book Rating : 4.:/5 (377 download)

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Book Synopsis Stability of Quasi-linear Hyperbolic Dissipative Systems by : Heinz Kreiss

Download or read book Stability of Quasi-linear Hyperbolic Dissipative Systems written by Heinz Kreiss and published by . This book was released on 1996 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fluids Under Control

Author : Tomáš Bodnár
Publisher : Springer Nature
ISBN 13 : 3031473558
Total Pages : 376 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis Fluids Under Control by : Tomáš Bodnár

Download or read book Fluids Under Control written by Tomáš Bodnár and published by Springer Nature. This book was released on with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Synchronization in Infinite-Dimensional Deterministic and Stochastic Systems

Author : Igor Chueshov
Publisher : Springer Nature
ISBN 13 : 3030470911
Total Pages : 346 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Synchronization in Infinite-Dimensional Deterministic and Stochastic Systems by : Igor Chueshov

Download or read book Synchronization in Infinite-Dimensional Deterministic and Stochastic Systems written by Igor Chueshov and published by Springer Nature. This book was released on 2020-07-29 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main goal of this book is to systematically address the mathematical methods that are applied in the study of synchronization of infinite-dimensional evolutionary dissipative or partially dissipative systems. It bases its unique monograph presentation on both general and abstract models and covers several important classes of coupled nonlinear deterministic and stochastic PDEs which generate infinite-dimensional dissipative systems. This text, which adapts readily to advanced graduate coursework in dissipative dynamics, requires some background knowledge in evolutionary equations and introductory functional analysis as well as a basic understanding of PDEs and the theory of random processes. Suitable for researchers in synchronization theory, the book is also relevant to physicists and engineers interested in both the mathematical background and the methods for the asymptotic analysis of coupled infinite-dimensional dissipative systems that arise in continuum mechanics.

Asymptotic Behavior of Dissipative Systems

Author : Jack K. Hale
Publisher :
ISBN 13 : 9781470412524
Total Pages : 210 pages
Book Rating : 4.4/5 (125 download)

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Book Synopsis Asymptotic Behavior of Dissipative Systems by : Jack K. Hale

Download or read book Asymptotic Behavior of Dissipative Systems written by Jack K. Hale and published by . This book was released on 2014-06-29 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is directed at researchers in nonlinear ordinary and partial differential equations and at those who apply these topics to other fields of science. About one third of the book focuses on the existence and properties of the flow on the global attractor for a discrete or continuous dynamical system. The author presents a detailed discussion of abstract properties and examples of asymptotically smooth maps and semigroups. He also covers some of the continuity properties of the global attractor under perturbation, its capacity and Hausdorff dimension, and the stability of the flow on the global attractor under perturbation. The remainder of the book deals with particular equations occurring in applications and especially emphasizes delay equations, reaction-diffusion equations, and the damped wave equations. In each of the examples presented, the author shows how to verify the existence of a global attractor, and, for several examples, he discusses some properties of the flow on the global attractor. Table of Contents: Introduction.Discrete dynamical systems: Limit sets; Stability of invariant sets and asymptotically smooth maps; Examples of asymptotically smooth maps; Dissipativeness and global attractors; Dependence on parameters; Fixed point theorems; Stability relative to the global attractor and Morse-Smale maps; Dimension of the global attractor; Dissipativeness in two spaces; Notes and remarks. Continuous dynamical systems: Limit sets; Asymptotically smooth and $\alpha$-contracting semigroups; Stability of invariant sets; Dissipativeness and global attractors; Dependence on parameters; Periodic processes; Skew product flows; Gradient flows; Dissipativeness in two spaces; Properties of the flow on the global attractor; Notes and remarks. Applications: Retarded functional differential equations; Sectorial evolutionary equations; A scalar parabolic equation; The Navier-Stokes equation; Neutral functional differential equations; Some abstract evolutionary equations; A one-dimensional damped wave equation; A three-dimensional damped wave equation; Remarks on other applications; Dependence on parameters and approximation of the attractor. Appendix. Stable and unstable manifolds. References. Index.This is a reprint of the 1988 original. Review from Zentralblatt MATH: This monograph reports the advances that have been made in the area by the author and many other mathematicians; it is an important source of ideas for the researchers interested in the subject. Review from Mathematical Reviews: Although advanced, this book is a very good introduction to the subject, and the reading of the abstract part, which is elegant, is pleasant...this monograph will be of valuable interest for those who aim to learn in the very rapidly growing subject of infinite-dimensional dissipative dynamical systems. (SURV/25.S)

Patterns and Interfaces in Dissipative Dynamics

Author : Len Pismen
Publisher : Springer Nature
ISBN 13 : 303129579X
Total Pages : 402 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Patterns and Interfaces in Dissipative Dynamics by : Len Pismen

Download or read book Patterns and Interfaces in Dissipative Dynamics written by Len Pismen and published by Springer Nature. This book was released on 2023-06-12 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spontaneous pattern formation in nonlinear dissipative systems far from equilibrium occurs in a variety of settings in nature and technology, and has applications ranging from nonlinear optics through solid and fluid mechanics, physical chemistry and chemical engineering to biology. This book explores the forefront of current research, describing in-depth the analytical methods that elucidate the complex evolution of nonlinear dissipative systems.

Quantum Dissipative Systems (Fifth Edition)

Author : Ulrich Weiss
Publisher : World Scientific
ISBN 13 : 9811241511
Total Pages : 607 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Quantum Dissipative Systems (Fifth Edition) by : Ulrich Weiss

Download or read book Quantum Dissipative Systems (Fifth Edition) written by Ulrich Weiss and published by World Scientific. This book was released on 2021-09-21 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.