Qualitative Theory Of Dynamical Systems Vol 6 N M 2
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Chaos In Automatic Control
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Author : Wilfrid Perruquetti
language : en
Publisher: CRC Press
Release Date : 2018-10-03
Chaos In Automatic Control written by Wilfrid Perruquetti and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-03 with Technology & Engineering categories.
Chaotic behavior arises in a variety of control settings. In some cases, it is beneficial to remove this behavior; in others, introducing or taking advantage of the existing chaotic components can be useful for example in cryptography. Chaos in Automatic Control surveys the latest methods for inserting, taking advantage of, or removing chaos in a variety of applications. This book supplies the theoretical and pedagogical basis of chaos in control systems along with new concepts and recent developments in the field. Presented in three parts, the book examines open-loop analysis, closed-loop control, and applications of chaos in control systems. The first section builds a background in the mathematics of ordinary differential and difference equations on which the remainder of the book is based. It includes an introductory chapter by Christian Mira, a pioneer in chaos research. The next section explores solutions to problems arising in observation and control of closed-loop chaotic control systems. These include model-independent control methods, strategies such as H-infinity and sliding modes, polytopic observers, normal forms using homogeneous transformations, and observability normal forms. The final section explores applications in wireless transmission, optics, power electronics, and cryptography. Chaos in Automatic Control distills the latest thinking in chaos while relating it to the most recent developments and applications in control. It serves as a platform for developing more robust, autonomous, intelligent, and adaptive systems.
Nonlinear Dynamical Systems
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Author : Irwin W. Sandberg
language : en
Publisher: John Wiley & Sons
Release Date : 2001-02-21
Nonlinear Dynamical Systems written by Irwin W. Sandberg 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 2001-02-21 with Technology & Engineering categories.
The first truly up-to-date look at the theory and capabilities of nonlinear dynamical systems that take the form of feedforward neural network structures Considered one of the most important types of structures in the study of neural networks and neural-like networks, feedforward networks incorporating dynamical elements have important properties and are of use in many applications. Specializing in experiential knowledge, a neural network stores and expands its knowledge base via strikingly human routes-through a learning process and information storage involving interconnection strengths known as synaptic weights. In Nonlinear Dynamical Systems: Feedforward Neural Network Perspectives, six leading authorities describe recent contributions to the development of an analytical basis for the understanding and use of nonlinear dynamical systems of the feedforward type, especially in the areas of control, signal processing, and time series analysis. Moving from an introductory discussion of the different aspects of feedforward neural networks, the book then addresses: * Classification problems and the related problem of approximating dynamic nonlinear input-output maps * The development of robust controllers and filters * The capability of neural networks to approximate functions and dynamic systems with respect to risk-sensitive error * Segmenting a time series It then sheds light on the application of feedforward neural networks to speech processing, summarizing speech-related techniques, and reviewing feedforward neural networks from the viewpoint of fundamental design issues. An up-to-date and authoritative look at the ever-widening technical boundaries and influence of neural networks in dynamical systems, this volume is an indispensable resource for researchers in neural networks and a reference staple for libraries.
Dynamical Systems And Related Topics
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Author : Evgeniĭ Frolovich Mishchenko
language : en
Publisher:
Release Date : 1997
Dynamical Systems And Related Topics written by Evgeniĭ Frolovich Mishchenko and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Differentiable dynamical systems categories.
Nonlinear Oscillations Dynamical Systems And Bifurcations Of Vector Fields
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Author : John Guckenheimer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-21
Nonlinear Oscillations Dynamical Systems And Bifurcations Of Vector Fields written by John Guckenheimer 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 2013-11-21 with Mathematics categories.
From the reviews: "This book is concerned with the application of methods from dynamical systems and bifurcation theories to the study of nonlinear oscillations. Chapter 1 provides a review of basic results in the theory of dynamical systems, covering both ordinary differential equations and discrete mappings. Chapter 2 presents 4 examples from nonlinear oscillations. Chapter 3 contains a discussion of the methods of local bifurcation theory for flows and maps, including center manifolds and normal forms. Chapter 4 develops analytical methods of averaging and perturbation theory. Close analysis of geometrically defined two-dimensional maps with complicated invariant sets is discussed in chapter 5. Chapter 6 covers global homoclinic and heteroclinic bifurcations. The final chapter shows how the global bifurcations reappear in degenerate local bifurcations and ends with several more models of physical problems which display these behaviors." #Book Review - Engineering Societies Library, New York#1 "An attempt to make research tools concerning `strange attractors' developed in the last 20 years available to applied scientists and to make clear to research mathematicians the needs in applied works. Emphasis on geometric and topological solutions of differential equations. Applications mainly drawn from nonlinear oscillations." #American Mathematical Monthly#2
Ordinary Differential Equations And Dynamical Systems
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Author : Gerald Teschl
language : en
Publisher: American Mathematical Society
Release Date : 2024-01-12
Ordinary Differential Equations And Dynamical Systems written by Gerald Teschl and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-12 with Mathematics categories.
This book provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students. The first part begins with some simple examples of explicitly solvable equations and a first glance at qualitative methods. Then the fundamental results concerning the initial value problem are proved: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore, linear equations are considered, including the Floquet theorem, and some perturbation results. As somewhat independent topics, the Frobenius method for linear equations in the complex domain is established and Sturm–Liouville boundary value problems, including oscillation theory, are investigated. The second part introduces the concept of a dynamical system. The Poincaré–Bendixson theorem is proved, and several examples of planar systems from classical mechanics, ecology, and electrical engineering are investigated. Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed. Finally, stability is studied, including the stable manifold and the Hartman–Grobman theorem for both continuous and discrete systems. The third part introduces chaos, beginning with the basics for iterated interval maps and ending with the Smale–Birkhoff theorem and the Melnikov method for homoclinic orbits. The text contains almost three hundred exercises. Additionally, the use of mathematical software systems is incorporated throughout, showing how they can help in the study of differential equations.
Nonlinear Dynamical Systems And Chaos
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Author : H.W. Broer
language : en
Publisher: Birkhäuser
Release Date : 2013-11-11
Nonlinear Dynamical Systems And Chaos written by H.W. Broer and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
Symmetries in dynamical systems, "KAM theory and other perturbation theories", "Infinite dimensional systems", "Time series analysis" and "Numerical continuation and bifurcation analysis" were the main topics of the December 1995 Dynamical Systems Conference held in Groningen in honour of Johann Bernoulli. They now form the core of this work which seeks to present the state of the art in various branches of the theory of dynamical systems. A number of articles have a survey character whereas others deal with recent results in current research. It contains interesting material for all members of the dynamical systems community, ranging from geometric and analytic aspects from a mathematical point of view to applications in various sciences.
Encyclopaedia Of Mathematics
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Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Encyclopaedia Of Mathematics written by Michiel Hazewinkel 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 2013-12-01 with Mathematics categories.
This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Discrete And Continuous Dynamical Systems
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Author :
language : en
Publisher:
Release Date : 2002
Discrete And Continuous Dynamical Systems written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Differentiable dynamical systems categories.
Foundations Of Mechanics
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Author : Ralph Abraham
language : en
Publisher: CRC Press
Release Date : 2019-04-24
Foundations Of Mechanics written by Ralph Abraham and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-24 with Science categories.
Foundations of Mechanics is a mathematical exposition of classical mechanics with an introduction to the qualitative theory of dynamical systems and applications to the two-body problem and three-body problem.
Golden Non Euclidean Geometry The Hilbert S Fourth Problem Golden Dynamical Systems And The Fine Structure Constant
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Author : Alexey Stakhov
language : en
Publisher: World Scientific
Release Date : 2016-07-14
Golden Non Euclidean Geometry The Hilbert S Fourth Problem Golden Dynamical Systems And The Fine Structure Constant written by Alexey Stakhov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-14 with Mathematics categories.
This unique book overturns our ideas about non-Euclidean geometry and the fine-structure constant, and attempts to solve long-standing mathematical problems. It describes a general theory of 'recursive' hyperbolic functions based on the 'Mathematics of Harmony,' and the 'golden,' 'silver,' and other 'metallic' proportions. Then, these theories are used to derive an original solution to Hilbert's Fourth Problem for hyperbolic and spherical geometries. On this journey, the book describes the 'golden' qualitative theory of dynamical systems based on 'metallic' proportions. Finally, it presents a solution to a Millennium Problem by developing the Fibonacci special theory of relativity as an original physical-mathematical solution for the fine-structure constant. It is intended for a wide audience who are interested in the history of mathematics, non-Euclidean geometry, Hilbert's mathematical problems, dynamical systems, and Millennium Problems.See Press Release: Application of the mathematics of harmony - Golden non-Euclidean geometry in modern math