Nonlinear Dynamical Systems And Chaos

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Nonlinear Dynamics and Chaos

Steven H. Strogatz
Nonlinear Dynamics and Chaos Book PDF

Author : Steven H. Strogatz
Publisher : CRC Press
Page : 532 pages
File Size : 45,8 Mb
Release : 2018-05-04
Category : Mathematics
ISBN : 9780429961113

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Nonlinear Dynamics and Chaos by Steven H. Strogatz Pdf

This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

Introduction to Applied Nonlinear Dynamical Systems and Chaos

Stephen Wiggins
Introduction to Applied Nonlinear Dynamical Systems and Chaos Book PDF

Author : Stephen Wiggins
Publisher : Springer Science & Business Media
Page : 844 pages
File Size : 49,6 Mb
Release : 2006-04-18
Category : Mathematics
ISBN : 9780387217499

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Introduction to Applied Nonlinear Dynamical Systems and Chaos by Stephen Wiggins Pdf

This introduction to applied nonlinear dynamics and chaos places emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about their behavior. The new edition has been updated and extended throughout, and contains a detailed glossary of terms. From the reviews: "Will serve as one of the most eminent introductions to the geometric theory of dynamical systems." --Monatshefte für Mathematik

An Exploration of Dynamical Systems and Chaos

John H. Argyris,Gunter Faust,Maria Haase,Rudolf Friedrich
An Exploration of Dynamical Systems and Chaos Book PDF

Author : John H. Argyris,Gunter Faust,Maria Haase,Rudolf Friedrich
Publisher : Springer
Page : 865 pages
File Size : 41,9 Mb
Release : 2015-04-24
Category : Technology & Engineering
ISBN : 9783662460429

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An Exploration of Dynamical Systems and Chaos by John H. Argyris,Gunter Faust,Maria Haase,Rudolf Friedrich Pdf

This book is conceived as a comprehensive and detailed text-book on non-linear dynamical systems with particular emphasis on the exploration of chaotic phenomena. The self-contained introductory presentation is addressed both to those who wish to study the physics of chaotic systems and non-linear dynamics intensively as well as those who are curious to learn more about the fascinating world of chaotic phenomena. Basic concepts like Poincaré section, iterated mappings, Hamiltonian chaos and KAM theory, strange attractors, fractal dimensions, Lyapunov exponents, bifurcation theory, self-similarity and renormalisation and transitions to chaos are thoroughly explained. To facilitate comprehension, mathematical concepts and tools are introduced in short sub-sections. The text is supported by numerous computer experiments and a multitude of graphical illustrations and colour plates emphasising the geometrical and topological characteristics of the underlying dynamics. This volume is a completely revised and enlarged second edition which comprises recently obtained research results of topical interest, and has been extended to include a new section on the basic concepts of probability theory. A completely new chapter on fully developed turbulence presents the successes of chaos theory, its limitations as well as future trends in the development of complex spatio-temporal structures. "This book will be of valuable help for my lectures" Hermann Haken, Stuttgart "This text-book should not be missing in any introductory lecture on non-linear systems and deterministic chaos" Wolfgang Kinzel, Würzburg “This well written book represents a comprehensive treatise on dynamical systems. It may serve as reference book for the whole field of nonlinear and chaotic systems and reports in a unique way on scientific developments of recent decades as well as important applications.” Joachim Peinke, Institute of Physics, Carl-von-Ossietzky University Oldenburg, Germany

An Introduction to Dynamical Systems and Chaos

G.C. Layek
An Introduction to Dynamical Systems and Chaos Book PDF

Author : G.C. Layek
Publisher : Springer
Page : 622 pages
File Size : 48,8 Mb
Release : 2015-12-01
Category : Mathematics
ISBN : 9788132225560

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An Introduction to Dynamical Systems and Chaos by G.C. Layek Pdf

The book discusses continuous and discrete systems in systematic and sequential approaches for all aspects of nonlinear dynamics. The unique feature of the book is its mathematical theories on flow bifurcations, oscillatory solutions, symmetry analysis of nonlinear systems and chaos theory. The logically structured content and sequential orientation provide readers with a global overview of the topic. A systematic mathematical approach has been adopted, and a number of examples worked out in detail and exercises have been included. Chapters 1–8 are devoted to continuous systems, beginning with one-dimensional flows. Symmetry is an inherent character of nonlinear systems, and the Lie invariance principle and its algorithm for finding symmetries of a system are discussed in Chap. 8. Chapters 9–13 focus on discrete systems, chaos and fractals. Conjugacy relationship among maps and its properties are described with proofs. Chaos theory and its connection with fractals, Hamiltonian flows and symmetries of nonlinear systems are among the main focuses of this book. Over the past few decades, there has been an unprecedented interest and advances in nonlinear systems, chaos theory and fractals, which is reflected in undergraduate and postgraduate curricula around the world. The book is useful for courses in dynamical systems and chaos, nonlinear dynamics, etc., for advanced undergraduate and postgraduate students in mathematics, physics and engineering.

Chaos

Kathleen Alligood,Tim Sauer,J.A. Yorke
Chaos Book PDF

Author : Kathleen Alligood,Tim Sauer,J.A. Yorke
Publisher : Springer
Page : 620 pages
File Size : 55,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642592812

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Chaos by Kathleen Alligood,Tim Sauer,J.A. Yorke Pdf

BACKGROUND Sir Isaac Newton hrought to the world the idea of modeling the motion of physical systems with equations. It was necessary to invent calculus along the way, since fundamental equations of motion involve velocities and accelerations, of position. His greatest single success was his discovery that which are derivatives the motion of the planets and moons of the solar system resulted from a single fundamental source: the gravitational attraction of the hodies. He demonstrated that the ohserved motion of the planets could he explained hy assuming that there is a gravitational attraction he tween any two ohjects, a force that is proportional to the product of masses and inversely proportional to the square of the distance between them. The circular, elliptical, and parabolic orhits of astronomy were v INTRODUCTION no longer fundamental determinants of motion, but were approximations of laws specified with differential equations. His methods are now used in modeling motion and change in all areas of science. Subsequent generations of scientists extended the method of using differ ential equations to describe how physical systems evolve. But the method had a limitation. While the differential equations were sufficient to determine the behavior-in the sense that solutions of the equations did exist-it was frequently difficult to figure out what that behavior would be. It was often impossible to write down solutions in relatively simple algebraic expressions using a finite number of terms. Series solutions involving infinite sums often would not converge beyond some finite time.

Nonlinear Dynamics and Chaos

J. M. T. Thompson,H. B. Stewart
Nonlinear Dynamics and Chaos Book PDF

Author : J. M. T. Thompson,H. B. Stewart
Publisher : John Wiley & Sons
Page : 492 pages
File Size : 43,8 Mb
Release : 2002-02-15
Category : Science
ISBN : 0471876844

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Nonlinear Dynamics and Chaos by J. M. T. Thompson,H. B. Stewart Pdf

Ein angesehener Bestseller - jetzt in der 2.aktualisierten Auflage! In diesem Buch finden Sie die aktuellsten Forschungsergebnisse auf dem Gebiet nichtlinearer Dynamik und Chaos, einem der am schnellsten wachsenden Teilgebiete der Mathematik. Die seit der ersten Auflage hinzugekommenen Erkenntnisse sind in einem zusätzlichen Kapitel übersichtlich zusammengefasst.

Chaos and Integrability in Nonlinear Dynamics

Michael Tabor
Chaos and Integrability in Nonlinear Dynamics Book PDF

Author : Michael Tabor
Publisher : Wiley-Interscience
Page : 392 pages
File Size : 54,6 Mb
Release : 1989-01-18
Category : Mathematics
ISBN : UOM:39015015760393

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Chaos and Integrability in Nonlinear Dynamics by Michael Tabor Pdf

Presents the newer field of chaos in nonlinear dynamics as a natural extension of classical mechanics as treated by differential equations. Employs Hamiltonian systems as the link between classical and nonlinear dynamics, emphasizing the concept of integrability. Also discusses nonintegrable dynamics, the fundamental KAM theorem, integrable partial differential equations, and soliton dynamics.

Nonlinear Dynamics, Chaos, and Complexity

Dimitri Volchenkov
Nonlinear Dynamics Chaos and Complexity Book PDF

Author : Dimitri Volchenkov
Publisher : Springer Nature
Page : 198 pages
File Size : 48,8 Mb
Release : 2020-12-14
Category : Mathematics
ISBN : 9789811590344

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Nonlinear Dynamics, Chaos, and Complexity by Dimitri Volchenkov Pdf

This book demonstrates how mathematical methods and techniques can be used in synergy and create a new way of looking at complex systems. It becomes clear nowadays that the standard (graph-based) network approach, in which observable events and transportation hubs are represented by nodes and relations between them are represented by edges, fails to describe the important properties of complex systems, capture the dependence between their scales, and anticipate their future developments. Therefore, authors in this book discuss the new generalized theories capable to describe a complex nexus of dependences in multi-level complex systems and to effectively engineer their important functions. The collection of works devoted to the memory of Professor Valentin Afraimovich introduces new concepts, methods, and applications in nonlinear dynamical systems covering physical problems and mathematical modelling relevant to molecular biology, genetics, neurosciences, artificial intelligence as well as classic problems in physics, machine learning, brain and urban dynamics. The book can be read by mathematicians, physicists, complex systems scientists, IT specialists, civil engineers, data scientists, urban planners, and even musicians (with some mathematical background).

Applications of Chaos and Nonlinear Dynamics in Engineering -

Santo Banerjee,Mala Mitra,Lamberto Rondoni
Applications of Chaos and Nonlinear Dynamics in Engineering Book PDF

Author : Santo Banerjee,Mala Mitra,Lamberto Rondoni
Publisher : Springer Science & Business Media
Page : 349 pages
File Size : 43,9 Mb
Release : 2011-09-10
Category : Technology & Engineering
ISBN : 9783642219214

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Applications of Chaos and Nonlinear Dynamics in Engineering - by Santo Banerjee,Mala Mitra,Lamberto Rondoni Pdf

Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, interdisciplinary quality of the insights gained in the last few decades has spawned myriad applications in almost all branches of science and technology—and even well beyond. Wherever quantitative modeling and analysis of complex, nonlinear phenomena is required, chaos theory and its methods can play a key role. This volume concentrates on reviewing the most relevant contemporary applications of chaotic nonlinear systems as they apply to the various cutting-edge branches of engineering. The book covers the theory as applied to robotics, electronic and communication engineering (for example chaos synchronization and cryptography) as well as to civil and mechanical engineering, where its use in damage monitoring and control is explored). Featuring contributions from active and leading research groups, this collection is ideal both as a reference and as a ‘recipe book’ full of tried and tested, successful engineering applications

Nonlinear Dynamics and Quantum Chaos

Sandro Wimberger
Nonlinear Dynamics and Quantum Chaos Book PDF

Author : Sandro Wimberger
Publisher : Springer
Page : 206 pages
File Size : 54,5 Mb
Release : 2014-05-13
Category : Science
ISBN : 9783319063430

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Nonlinear Dynamics and Quantum Chaos by Sandro Wimberger Pdf

The field of nonlinear dynamics and chaos has grown very much over the last few decades and is becoming more and more relevant in different disciplines. This book presents a clear and concise introduction to the field of nonlinear dynamics and chaos, suitable for graduate students in mathematics, physics, chemistry, engineering, and in natural sciences in general. It provides a thorough and modern introduction to the concepts of Hamiltonian dynamical systems' theory combining in a comprehensive way classical and quantum mechanical description. It covers a wide range of topics usually not found in similar books. Motivations of the respective subjects and a clear presentation eases the understanding. The book is based on lectures on classical and quantum chaos held by the author at Heidelberg University. It contains exercises and worked examples, which makes it ideal for an introductory course for students as well as for researchers starting to work in the field.

Nonlinear Dynamics

Muthusamy Lakshmanan,Shanmuganathan Rajaseekar
Nonlinear Dynamics Book PDF

Author : Muthusamy Lakshmanan,Shanmuganathan Rajaseekar
Publisher : Springer Science & Business Media
Page : 628 pages
File Size : 49,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642556883

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Nonlinear Dynamics by Muthusamy Lakshmanan,Shanmuganathan Rajaseekar Pdf

This self-contained treatment covers all aspects of nonlinear dynamics, from fundamentals to recent developments, in a unified and comprehensive way. Numerous examples and exercises will help the student to assimilate and apply the techniques presented.

Understanding Nonlinear Dynamics

Daniel Kaplan,Leon Glass
Understanding Nonlinear Dynamics Book PDF

Author : Daniel Kaplan,Leon Glass
Publisher : Springer Science & Business Media
Page : 438 pages
File Size : 41,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461208235

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Understanding Nonlinear Dynamics by Daniel Kaplan,Leon Glass Pdf

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics ( TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. About the Authors Daniel Kaplan specializes in the analysis of data using techniques motivated by nonlinear dynamics. His primary interest is in the interpretation of irregular physiological rhythms, but the methods he has developed have been used in geo physics, economics, marine ecology, and other fields. He joined McGill in 1991, after receiving his Ph.D from Harvard University and working at MIT. His un dergraduate studies were completed at Swarthmore College. He has worked with several instrumentation companies to develop novel types of medical monitors.

An Introduction to Symbolic Dynamics and Coding

Douglas Lind,Brian Marcus
An Introduction to Symbolic Dynamics and Coding Book PDF

Author : Douglas Lind,Brian Marcus
Publisher : Cambridge University Press
Page : 571 pages
File Size : 51,6 Mb
Release : 2021-01-21
Category : Language Arts & Disciplines
ISBN : 9781108820288

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An Introduction to Symbolic Dynamics and Coding by Douglas Lind,Brian Marcus Pdf

Elementary introduction to symbolic dynamics, updated to describe the main advances in the subject since the original publication in 1995.

Nonlinear Dynamics and Chaos

J Hogan,A.R Krauskopf,Mario di Bernado,R. Eddie Wilson,Hinke. M Osinga,Martin. E Homer,Alan. R Champneys
Nonlinear Dynamics and Chaos Book PDF

Author : J Hogan,A.R Krauskopf,Mario di Bernado,R. Eddie Wilson,Hinke. M Osinga,Martin. E Homer,Alan. R Champneys
Publisher : CRC Press
Page : 376 pages
File Size : 45,9 Mb
Release : 2002-08-01
Category : Science
ISBN : 9781420033830

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Nonlinear Dynamics and Chaos by J Hogan,A.R Krauskopf,Mario di Bernado,R. Eddie Wilson,Hinke. M Osinga,Martin. E Homer,Alan. R Champneys Pdf

Nonlinear dynamics has been successful in explaining complicated phenomena in well-defined low-dimensional systems. Now it is time to focus on real-life problems that are high-dimensional or ill-defined, for example, due to delay, spatial extent, stochasticity, or the limited nature of available data. How can one understand the dynamics of such systems? Written by international experts, Nonlinear Dynamics and Chaos: Where Do We Go from Here? assesses what the future holds for dynamics and chaos. The chapters address one or more of the broad and interconnected main themes: neural and biological systems, spatially extended systems, and experimentation in the physical sciences. The contributors offer suggestions as to what they see as the way forward, often in the form of open questions for future research.

Nonlinear Dynamics and Chaos: Advances and Perspectives

Marco Thiel,Jürgen Kurths,M. Carmen Romano,György Károlyi,Alessandro Moura
Nonlinear Dynamics and Chaos Advances and Perspectives Book PDF

Author : Marco Thiel,Jürgen Kurths,M. Carmen Romano,György Károlyi,Alessandro Moura
Publisher : Springer
Page : 293 pages
File Size : 44,6 Mb
Release : 2010-05-17
Category : Science
ISBN : 9783642046292

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Nonlinear Dynamics and Chaos: Advances and Perspectives by Marco Thiel,Jürgen Kurths,M. Carmen Romano,György Károlyi,Alessandro Moura Pdf

This book is a collection of papers contributed by some of the greatest names in the areas of chaos and nonlinear dynamics. Each paper examines a research topic at the frontier of the area of dynamical systems. As well as reviewing recent results, each paper also discusses the future perspectives of each topic. The result is an invaluable snapshot of the state of the ?eld by some of the most important researchers in the area. The ?rst contribution in this book (the section entitled “How did you get into Chaos?”) is actually not a paper, but a collection of personal accounts by a number of participants of the conference held in Aberdeen in September 2007 to honour Celso Grebogi’s 60th birthday. At the instigation of James Yorke, many of the most well-known scientists in the area agreed to share their tales on how they got involved in chaos during a celebratory dinner in Celso’s honour during the conference. This was recorded in video, we felt that these accounts were a valuable historic document for the ?eld. So we decided to transcribe it and include it here as the ?rst section of the book.