Infinite Dimensional Dynamical Systems
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Infinite Dimensional Dynamical Systems In Mechanics And Physics
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Author : Roger Temam
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11
Infinite Dimensional Dynamical Systems In Mechanics And Physics written by Roger Temam 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 2013-12-11 with Mathematics categories.
In this book the author presents the dynamical systems in infinite dimension, especially those generated by dissipative partial differential equations. This book attempts a systematic study of infinite dimensional dynamical systems generated by dissipative evolution partial differential equations arising in mechanics and physics and in other areas of sciences and technology. This second edition has been updated and extended.
Local Bifurcations Center Manifolds And Normal Forms In Infinite Dimensional Dynamical Systems
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Author : Mariana Haragus
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-23
Local Bifurcations Center Manifolds And Normal Forms In Infinite Dimensional Dynamical Systems written by Mariana Haragus 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 2010-11-23 with Mathematics categories.
An extension of different lectures given by the authors, Local Bifurcations, Center Manifolds, and Normal Forms in Infinite Dimensional Dynamical Systems provides the reader with a comprehensive overview of these topics. Starting with the simplest bifurcation problems arising for ordinary differential equations in one- and two-dimensions, this book describes several tools from the theory of infinite dimensional dynamical systems, allowing the reader to treat more complicated bifurcation problems, such as bifurcations arising in partial differential equations. Attention is restricted to the study of local bifurcations with a focus upon the center manifold reduction and the normal form theory; two methods that have been widely used during the last decades. Through use of step-by-step examples and exercises, a number of possible applications are illustrated, and allow the less familiar reader to use this reduction method by checking some clear assumptions. Written by recognised experts in the field of center manifold and normal form theory this book provides a much-needed graduate level text on bifurcation theory, center manifolds and normal form theory. It will appeal to graduate students and researchers working in dynamical system theory.
Dynamics In Infinite Dimensions
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Author : Jack K. Hale
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-18
Dynamics In Infinite Dimensions written by Jack K. Hale 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 2006-04-18 with Mathematics categories.
State-of-the-art in qualitative theory of functional differential equations; Most of the new material has never appeared in book form and some not even in papers; Second edition updated with new topics and results; Methods discussed will apply to other equations and applications
Stability Of Dynamical Systems
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Author :
language : en
Publisher: Springer Science & Business Media
Release Date : 2008
Stability Of Dynamical Systems written by 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 2008 with Differentiable dynamical systems categories.
In the analysis and synthesis of contemporary systems, engineers and scientists are frequently confronted with increasingly complex models that may simultaneously include components whose states evolve along continuous time and discrete instants; components whose descriptions may exhibit nonlinearities, time lags, transportation delays, hysteresis effects, and uncertainties in parameters; and components that cannot be described by various classical equations, as in the case of discrete-event systems, logic commands, and Petri nets. The qualitative analysis of such systems requires results for finite-dimensional and infinite-dimensional systems; continuous-time and discrete-time systems; continuous continuous-time and discontinuous continuous-time systems; and hybrid systems involving a mixture of continuous and discrete dynamics. Filling a gap in the literature, this textbook presents the first comprehensive stability analysis of all the major types of system models described above. Throughout the book, the applicability of the developed theory is demonstrated by means of many specific examples and applications to important classes of systems, including digital control systems, nonlinear regulator systems, pulse-width-modulated feedback control systems, artificial neural networks (with and without time delays), digital signal processing, a class of discrete-event systems (with applications to manufacturing and computer load balancing problems) and a multicore nuclear reactor model. The book covers the following four general topics: * Representation and modeling of dynamical systems of the types described above * Presentation of Lyapunov and Lagrange stability theory for dynamical systems defined on general metric spaces * Specialization of this stability theory to finite-dimensional dynamical systems * Specialization of this stability theory to infinite-dimensional dynamical systems Replete with exercises and requiring basic knowledge of linear algebra, analysis, and differential equations, the work may be used as a textbook for graduate courses in stability theory of dynamical systems. The book may also serve as a self-study reference for graduate students, researchers, and practitioners in applied mathematics, engineering, computer science, physics, chemistry, biology, and economics.
An Introduction To Infinite Dimensional Analysis
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Author : Giuseppe Da Prato
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-08-25
An Introduction To Infinite Dimensional Analysis written by Giuseppe Da Prato 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 2006-08-25 with Mathematics categories.
Based on well-known lectures given at Scuola Normale Superiore in Pisa, this book introduces analysis in a separable Hilbert space of infinite dimension. It starts from the definition of Gaussian measures in Hilbert spaces, concepts such as the Cameron-Martin formula, Brownian motion and Wiener integral are introduced in a simple way. These concepts are then used to illustrate basic stochastic dynamical systems and Markov semi-groups, paying attention to their long-time behavior.
Stability And Stabilization Of Infinite Dimensional Systems With Applications
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Author : Zheng-Hua Luo
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-01-22
Stability And Stabilization Of Infinite Dimensional Systems With Applications written by Zheng-Hua Luo 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 1999-01-22 with Computers categories.
The time evol11tion of many physical phenomena in nat11re can be de scribed by partial differential eq11ations. To analyze and control the dynamic behavior of s11ch systems. infinite dimensional system theory was developed and has been refined over the past several decades. In recent years. stim11lated by the applications arising from space exploration. a11tomated manufact11ring, and other areas of technological advancement, major progress has been made in both theory and control technology associated with infinite dimensional systems. For example, new conditions in the time domain and frequency domain have been derived which guarantee that a Co-semigroup is exponen tially stable; new feedback control laws helVe been proposed to exponentially ;;tabilize beam. wave, and thermoelastic equations; and new methods have been developed which allow us to show that the spectrum-determined growth condition holds for a wide class of systems. Therefore, there is a need for a reference book which presents these restllts in an integrated fashion. Complementing the existing books, e. g . . [1]. [41]. and [128]. this book reports some recent achievements in stability and feedback stabilization of infinite dimensional systems. In particular, emphasis will be placed on the second order partial differential equations. such as Euler-Bernoulli beam equations. which arise from control of numerous mechanical systems stich as flexible robot arms and large space structures. We will be focusing on new results. most of which are our own recently obtained research results.
Linear Port Hamiltonian Systems On Infinite Dimensional Spaces
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Author : Birgit Jacob
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-06-13
Linear Port Hamiltonian Systems On Infinite Dimensional Spaces written by Birgit Jacob 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 2012-06-13 with Science categories.
This book provides a self-contained introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems. The textbook starts with elementary known results, then progresses smoothly to advanced topics in current research. Many physical systems can be formulated using a Hamiltonian framework, leading to models described by ordinary or partial differential equations. For the purpose of control and for the interconnection of two or more Hamiltonian systems it is essential to take into account this interaction with the environment. This book is the first textbook on infinite-dimensional port-Hamiltonian systems. An abstract functional analytical approach is combined with the physical approach to Hamiltonian systems. This combined approach leads to easily verifiable conditions for well-posedness and stability. The book is accessible to graduate engineers and mathematicians with a minimal background in functional analysis. Moreover, the theory is illustrated by many worked-out examples.
Ergodicity For Infinite Dimensional Systems
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Author : Giuseppe Da Prato
language : en
Publisher:
Release Date : 1996
Ergodicity For Infinite Dimensional Systems written by Giuseppe Da Prato and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.
The Connection Between Infinite Dimensional And Finite Dimensional Dynamical Systems
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Author : Basil Nicolaenko
language : en
Publisher: American Mathematical Soc.
Release Date : 1989
The Connection Between Infinite Dimensional And Finite Dimensional Dynamical Systems written by Basil Nicolaenko and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
The last few years have seen a number of major developments demonstrating that the long-term behavior of solutions of a very large class of partial differential equations possesses a striking resemblance to the behavior of solutions of finite dimensional dynamical systems, or ordinary differential equations. The first of these advances was the discovery that a dissipative PDE has a compact, global attractor with finite Hausdorff and fractal dimensions. More recently, it was shown that some of these PDEs possess a finite dimensional inertial manifold-that is, an invariant manifold containing the attractor and exponentially attractive trajectories. With the improved understanding of the exact connection between finite dimensional dynamical systems and various classes of dissipative PDEs, it is now realistic to hope that the wealth of studies of such topics as bifurcations of finite vector fields and ``strange'' fractal attractors can be brought to bear on various mathematical models, including continuum flows. Surprisingly, a number of distributed systems from continuum mechanics have been found to exhibit the same nontrivial dynamic behavior as observed in low-dimensional dynamical systems. As a natural consequence of these observations, a new direction of research has arisen: detection and analysis of finite dimensional dynamical characteristics of infinite-dimensional systems. This book represents the proceedings of an AMS-IMS-SIAM Summer Research Conference, held in July, 1987 at the University of Colorado at Boulder. Bringing together mathematicians and physicists, the conference provided a forum for presentations on the latest developments in the field and fostered lively interactions on open questions and future directions. With contributions from some of the top experts, these proceedings will provide readers with an overview of this vital area of research.