Handbook of Dynamical Systems

Handbook of Dynamical Systems
Author: H. Broer,F. Takens,B. Hasselblatt
Publsiher: Elsevier
Total Pages: 560
Release: 2010-11-10
ISBN 10: 9780080932262
ISBN 13: 0080932266
Language: EN, FR, DE, ES & NL

Handbook of Dynamical Systems Book Review:

In this volume, the authors present a collection of surveys on various aspects of the theory of bifurcations of differentiable dynamical systems and related topics. By selecting these subjects, they focus on those developments from which research will be active in the coming years. The surveys are intended to educate the reader on the recent literature on the following subjects: transversality and generic properties like the various forms of the so-called Kupka-Smale theorem, the Closing Lemma and generic local bifurcations of functions (so-called catastrophe theory) and generic local bifurcations in 1-parameter families of dynamical systems, and notions of structural stability and moduli. Covers recent literature on various topics related to the theory of bifurcations of differentiable dynamical systems Highlights developments that are the foundation for future research in this field Provides material in the form of surveys, which are important tools for introducing the bifurcations of differentiable dynamical systems

Handbook of Dynamical Systems

Handbook of Dynamical Systems
Author: A. Katok,B. Hasselblatt
Publsiher: Elsevier
Total Pages: 1234
Release: 2005-12-17
ISBN 10: 9780080478227
ISBN 13: 0080478220
Language: EN, FR, DE, ES & NL

Handbook of Dynamical Systems Book Review:

This second half of Volume 1 of this Handbook follows Volume 1A, which was published in 2002. The contents of these two tightly integrated parts taken together come close to a realization of the program formulated in the introductory survey “Principal Structures of Volume 1A. The present volume contains surveys on subjects in four areas of dynamical systems: Hyperbolic dynamics, parabolic dynamics, ergodic theory and infinite-dimensional dynamical systems (partial differential equations). . Written by experts in the field. . The coverage of ergodic theory in these two parts of Volume 1 is considerably more broad and thorough than that provided in other existing sources. . The final cluster of chapters discusses partial differential equations from the point of view of dynamical systems.

Handbook of Dynamical Systems

Handbook of Dynamical Systems
Author: B. Fiedler
Publsiher: Gulf Professional Publishing
Total Pages: 1098
Release: 2002-02-21
ISBN 10: 0080532845
ISBN 13: 9780080532844
Language: EN, FR, DE, ES & NL

Handbook of Dynamical Systems Book Review:

This handbook is volume II in a series collecting mathematical state-of-the-art surveys in the field of dynamical systems. Much of this field has developed from interactions with other areas of science, and this volume shows how concepts of dynamical systems further the understanding of mathematical issues that arise in applications. Although modeling issues are addressed, the central theme is the mathematically rigorous investigation of the resulting differential equations and their dynamic behavior. However, the authors and editors have made an effort to ensure readability on a non-technical level for mathematicians from other fields and for other scientists and engineers. The eighteen surveys collected here do not aspire to encyclopedic completeness, but present selected paradigms. The surveys are grouped into those emphasizing finite-dimensional methods, numerics, topological methods, and partial differential equations. Application areas include the dynamics of neural networks, fluid flows, nonlinear optics, and many others. While the survey articles can be read independently, they deeply share recurrent themes from dynamical systems. Attractors, bifurcations, center manifolds, dimension reduction, ergodicity, homoclinicity, hyperbolicity, invariant and inertial manifolds, normal forms, recurrence, shift dynamics, stability, to name just a few, are ubiquitous dynamical concepts throughout the articles.

Handbook of Dynamical Systems

Handbook of Dynamical Systems
Author: B. Hasselblatt,A. Katok
Publsiher: Elsevier
Total Pages: 1232
Release: 2002-08-20
ISBN 10: 0080533442
ISBN 13: 9780080533445
Language: EN, FR, DE, ES & NL

Handbook of Dynamical Systems Book Review:

Volumes 1A and 1B. These volumes give a comprehensive survey of dynamics written by specialists in the various subfields of dynamical systems. The presentation attains coherence through a major introductory survey by the editors that organizes the entire subject, and by ample cross-references between individual surveys. The volumes are a valuable resource for dynamicists seeking to acquaint themselves with other specialties in the field, and to mathematicians active in other branches of mathematics who wish to learn about contemporary ideas and results dynamics. Assuming only general mathematical knowledge the surveys lead the reader towards the current state of research in dynamics. Volume 1B will appear 2005.

Handbook of Dynamics and Probability

Handbook of Dynamics and Probability
Author: Peter Müller
Publsiher: Springer Nature
Total Pages: 543
Release: 2021-11-20
ISBN 10: 3030884864
ISBN 13: 9783030884864
Language: EN, FR, DE, ES & NL

Handbook of Dynamics and Probability Book Review:

Our time is characterized by an explosive growth in the use of ever more complicated and sophisticated (computer) models. These models rely on dynamical systems theory for the interpretation of their results and on probability theory for the quantification of their uncertainties. A conscientious and intelligent use of these models requires that both these theories are properly understood. This book is to provide such understanding. It gives a unifying treatment of dynamical systems theory and probability theory. It covers the basic concepts and statements of these theories, their interrelations, and their applications to scientific reasoning and physics. The book stresses the underlying concepts and mathematical structures but is written in a simple and illuminating manner without sacrificing too much mathematical rigor. The book is aimed at students, post-docs, and researchers in the applied sciences who aspire to better understand the conceptual and mathematical underpinnings of the models that they use. Despite the peculiarities of any applied science, dynamics and probability are the common and indispensable tools in any modeling effort. The book is self-contained, with many technical aspects covered in appendices, but does require some basic knowledge in analysis, linear algebra, and physics. Peter Müller, now a professor emeritus at the University of Hawaii, has worked extensively on ocean and climate models and the foundations of complex system theories.

Philosophy of Complex Systems

Philosophy of Complex Systems
Author: Anonim
Publsiher: Elsevier
Total Pages: 952
Release: 2011-05-23
ISBN 10: 9780080931227
ISBN 13: 0080931227
Language: EN, FR, DE, ES & NL

Philosophy of Complex Systems Book Review:

The domain of nonlinear dynamical systems and its mathematical underpinnings has been developing exponentially for a century, the last 35 years seeing an outpouring of new ideas and applications and a concomitant confluence with ideas of complex systems and their applications from irreversible thermodynamics. A few examples are in meteorology, ecological dynamics, and social and economic dynamics. These new ideas have profound implications for our understanding and practice in domains involving complexity, predictability and determinism, equilibrium, control, planning, individuality, responsibility and so on. Our intention is to draw together in this volume, we believe for the first time, a comprehensive picture of the manifold philosophically interesting impacts of recent developments in understanding nonlinear systems and the unique aspects of their complexity. The book will focus specifically on the philosophical concepts, principles, judgments and problems distinctly raised by work in the domain of complex nonlinear dynamical systems, especially in recent years. -Comprehensive coverage of all main theories in the philosophy of Complex Systems -Clearly written expositions of fundamental ideas and concepts -Definitive discussions by leading researchers in the field -Summaries of leading-edge research in related fields are also included

Dynamical Systems

Dynamical Systems
Author: Zeraoulia Elhadj
Publsiher: CRC Press
Total Pages: 400
Release: 2019-01-21
ISBN 10: 0429647425
ISBN 13: 9780429647420
Language: EN, FR, DE, ES & NL

Dynamical Systems Book Review:

Chaos is the idea that a system will produce very different long-term behaviors when the initial conditions are perturbed only slightly. Chaos is used for novel, time- or energy-critical interdisciplinary applications. Examples include high-performance circuits and devices, liquid mixing, chemical reactions, biological systems, crisis management, secure information processing, and critical decision-making in politics, economics, as well as military applications, etc. This book presents the latest investigations in the theory of chaotic systems and their dynamics. The book covers some theoretical aspects of the subject arising in the study of both discrete and continuous-time chaotic dynamical systems. This book presents the state-of-the-art of the more advanced studies of chaotic dynamical systems.

Handbook of dynamical systems

Handbook of dynamical systems
Author: Anonim
Publsiher: Unknown
Total Pages: 135
Release: 2010
ISBN 10: 1928374650XXX
ISBN 13: OCLC:944496750
Language: EN, FR, DE, ES & NL

Handbook of dynamical systems Book Review:

Handbook of Dynamic System Modeling

Handbook of Dynamic System Modeling
Author: Paul A. Fishwick
Publsiher: CRC Press
Total Pages: 760
Release: 2007-06-01
ISBN 10: 9781420010855
ISBN 13: 1420010859
Language: EN, FR, DE, ES & NL

Handbook of Dynamic System Modeling Book Review:

The topic of dynamic models tends to be splintered across various disciplines, making it difficult to uniformly study the subject. Moreover, the models have a variety of representations, from traditional mathematical notations to diagrammatic and immersive depictions. Collecting all of these expressions of dynamic models, the Handbook of Dynamic System Modeling explores a panoply of different types of modeling methods available for dynamical systems. Featuring an interdisciplinary, balanced approach, the handbook focuses on both generalized dynamic knowledge and specific models. It first introduces the general concepts, representations, and philosophy of dynamic models, followed by a section on modeling methodologies that explains how to portray designed models on a computer. After addressing scale, heterogeneity, and composition issues, the book covers specific model types that are often characterized by specific visual- or text-based grammars. It concludes with case studies that employ two well-known commercial packages to construct, simulate, and analyze dynamic models. A complete guide to the fundamentals, types, and applications of dynamic models, this handbook shows how systems function and are represented over time and space and illustrates how to select a particular model based on a specific area of interest.

A Modern Introduction to Dynamical Systems

A Modern Introduction to Dynamical Systems
Author: Richard Brown
Publsiher: Oxford University Press
Total Pages: 432
Release: 2018-06-28
ISBN 10: 0198743289
ISBN 13: 9780198743286
Language: EN, FR, DE, ES & NL

A Modern Introduction to Dynamical Systems Book Review:

This text is a high-level introduction to the modern theory of dynamical systems; an analysis-based, pure mathematics course textbook in the basic tools, techniques, theory and development of both the abstract and the practical notions of mathematical modelling, using both discrete and continuous concepts and examples comprising what may be called the modern theory of dynamics. Prerequisite knowledge is restricted to calculus, linear algebra and basic differential equations, and all higher-level analysis, geometry and algebra is introduced as needed within the text. Following this text from start to finish will provide the careful reader with the tools, vocabulary and conceptual foundation necessary to continue in further self-study and begin to explore current areas of active research in dynamical systems.

Chaos and Dynamical Systems

Chaos and Dynamical Systems
Author: David Feldman
Publsiher: Princeton University Press
Total Pages: 264
Release: 2019-08-06
ISBN 10: 0691161526
ISBN 13: 9780691161525
Language: EN, FR, DE, ES & NL

Chaos and Dynamical Systems Book Review:

The author presents an accessible, clear introduction to dynamical systems and chaos theory, important and exciting areas that have shaped many scientific fields. While the rules governing dynamical systems are well-specified and simple, the behavior of many dynamical systems is remarkably complex.

Handbook of Hybrid Systems Control

Handbook of Hybrid Systems Control
Author: Jan Lunze,Françoise Lamnabhi-Lagarrigue
Publsiher: Cambridge University Press
Total Pages: 565
Release: 2009-10-15
ISBN 10: 0521765056
ISBN 13: 9780521765053
Language: EN, FR, DE, ES & NL

Handbook of Hybrid Systems Control Book Review:

Setting out core theory and reviewing a range of new methods, theoretical problems and applications, this handbook shows how hybrid dynamical systems can be modelled and understood. Sixty expert authors involved in the recent research activities and industrial application studies provide practical insights on topics ranging from the theoretical investigations over computer-aided design to applications in energy management and the process industry. Structured into three parts, the book opens with a thorough introduction to hybrid systems theory, illustrating new dynamical phenomena through numerous examples. Part II then provides a survey of key tools and tool integration activities. Finally, Part III is dedicated to applications, implementation issues and system integration, considering different domains such as industrial control, automotive systems and digital networks. Three running examples are referred to throughout the book, together with numerous illustrations, helping both researchers and industry professionals to understand complex theory, recognise problems and find appropriate solutions.

Qualitative Theory of Dynamical Systems

Qualitative Theory of Dynamical Systems
Author: Anthony Michel,Anthony Wang,Bo Hu,Zuhair Nashed,Earl Taft
Publsiher: CRC Press
Total Pages: 732
Release: 2001-01-04
ISBN 10: 9780203908297
ISBN 13: 0203908295
Language: EN, FR, DE, ES & NL

Qualitative Theory of Dynamical Systems Book Review:

"Illuminates the most important results of the Lyapunov and Lagrange stability theory for a general class of dynamical systems by developing topics in a metric space independantly of equations, inequalities, or inclusions. Applies the general theory to specific classes of equations. Presents new and expanded material on the stability analysis of hybrid dynamical systems and dynamical systems with discontinuous dynamics."

Dynamical Systems in Neuroscience

Dynamical Systems in Neuroscience
Author: Eugene M. Izhikevich
Publsiher: MIT Press
Total Pages: 458
Release: 2010-01-22
ISBN 10: 0262514206
ISBN 13: 9780262514200
Language: EN, FR, DE, ES & NL

Dynamical Systems in Neuroscience Book Review:

Explains the relationship of electrophysiology, nonlinear dynamics, and the computational properties of neurons, with each concept presented in terms of both neuroscience and mathematics and illustrated using geometrical intuition. In order to model neuronal behavior or to interpret the results of modeling studies, neuroscientists must call upon methods of nonlinear dynamics. This book offers an introduction to nonlinear dynamical systems theory for researchers and graduate students in neuroscience. It also provides an overview of neuroscience for mathematicians who want to learn the basic facts of electrophysiology. Dynamical Systems in Neuroscience presents a systematic study of the relationship of electrophysiology, nonlinear dynamics, and computational properties of neurons. It emphasizes that information processing in the brain depends not only on the electrophysiological properties of neurons but also on their dynamical properties. The book introduces dynamical systems, starting with one- and two-dimensional Hodgkin-Huxley-type models and continuing to a description of bursting systems. Each chapter proceeds from the simple to the complex, and provides sample problems at the end. The book explains all necessary mathematical concepts using geometrical intuition; it includes many figures and few equations, making it especially suitable for non-mathematicians. Each concept is presented in terms of both neuroscience and mathematics, providing a link between the two disciplines. Nonlinear dynamical systems theory is at the core of computational neuroscience research, but it is not a standard part of the graduate neuroscience curriculum—or taught by math or physics department in a way that is suitable for students of biology. This book offers neuroscience students and researchers a comprehensive account of concepts and methods increasingly used in computational neuroscience. An additional chapter on synchronization, with more advanced material, can be found at the author's website, www.izhikevich.com.

Dynamical Systems and Chaos

Dynamical Systems and Chaos
Author: Henk Broer,Floris Takens
Publsiher: Springer Science & Business Media
Total Pages: 313
Release: 2010-10-20
ISBN 10: 1441968709
ISBN 13: 9781441968708
Language: EN, FR, DE, ES & NL

Dynamical Systems and Chaos Book Review:

Over the last four decades there has been extensive development in the theory of dynamical systems. This book aims at a wide audience where the first four chapters have been used for an undergraduate course in Dynamical Systems. Material from the last two chapters and from the appendices has been used quite a lot for master and PhD courses. All chapters are concluded by an exercise section. The book is also directed towards researchers, where one of the challenges is to help applied researchers acquire background for a better understanding of the data that computer simulation or experiment may provide them with the development of the theory.

Chaos in Dynamical Systems

Chaos in Dynamical Systems
Author: Edward Ott
Publsiher: Cambridge University Press
Total Pages: 478
Release: 2002-08-22
ISBN 10: 9780521010849
ISBN 13: 0521010845
Language: EN, FR, DE, ES & NL

Chaos in Dynamical Systems Book Review:

New edition of the best-selling graduate textbook on chaos for scientists and engineers.

Discovering Discrete Dynamical Systems

Discovering Discrete Dynamical Systems
Author: Aimee Johnson,Kathleen Madden,Ayse Sahin
Publsiher: American Mathematical Soc.
Total Pages: 116
Release: 2017-12-31
ISBN 10: 1614441243
ISBN 13: 9781614441243
Language: EN, FR, DE, ES & NL

Discovering Discrete Dynamical Systems Book Review:

Discovering Discrete Dynamical Systems is a mathematics textbook designed for use in a student-led, inquiry-based course for advanced mathematics majors. Fourteen modules each with an opening exploration, a short exposition and related exercises, and a concluding project guide students to self-discovery on topics such as fixed points and their classifications, chaos and fractals, Julia and Mandelbrot sets in the complex plane, and symbolic dynamics. Topics have been carefully chosen as a means for developing student persistence and skill in exploration, conjecture, and generalization while at the same time providing a coherent introduction to the fundamentals of discrete dynamical systems. This book is written for undergraduate students with the prerequisites for a first analysis course, and it can easily be used by any faculty member in a mathematics department, regardless of area of expertise. Each module starts with an exploration in which the students are asked an open-ended question. This allows the students to make discoveries which lead them to formulate the questions that will be addressed in the exposition and exercises of the module. The exposition is brief and has been written with the intent that a student who has taken, or is ready to take, a course in analysis can read the material independently. The exposition concludes with exercises which have been designed to both illustrate and explore in more depth the ideas covered in the exposition. Each module concludes with a project in which students bring the ideas from the module to bear on a more challenging or in-depth problem. A section entitled "To the Instructor" includes suggestions on how to structure a course in order to realize the inquiry-based intent of the book. The book has also been used successfully as the basis for an independent study course and as a supplementary text for an analysis course with traditional content.

Dynamical Systems and Nonlinear Waves in Plasmas

Dynamical Systems and Nonlinear Waves in Plasmas
Author: Santo Banerjee,Asit Saha
Publsiher: CRC Press
Total Pages: 218
Release: 2021-09-10
ISBN 10: 1000404757
ISBN 13: 9781000404753
Language: EN, FR, DE, ES & NL

Dynamical Systems and Nonlinear Waves in Plasmas Book Review:

Dynamical systems and Nonlinear Waves in Plasmas is written in a clear and comprehensible style to serve as a compact volume for advanced postgraduate students and researchers working in the areas of Applied Physics, Applied Mathematics, Dynamical Systems, Nonlinear waves in Plasmas or other nonlinear media. It provides an introduction to the background of dynamical systems, waves, oscillations and plasmas. Basic concepts of dynamical systems and phase plane analysis for the study of dynamical properties of nonlinear waves in plasmas are presented. Different kinds of waves in plasmas are introduced. Reductive perturbative technique and its applications to derive different kinds of nonlinear evolution equations in plasmas are discussed. Analytical wave solutions of these nonlinear evolution equations are presented using the concept of bifurcation theory of planar dynamical systems in a very simple way. Bifurcations of both small and arbitrary amplitudes of various nonlinear acoustic waves in plasmas are presented using phase plots and time-series plots. Super nonlinear waves and its bifurcation behaviour are discussed for various plasma systems. Multiperiodic, quasiperiodic and chaotic motions of nonlinear plasma waves are discussed in presence of external periodic force. Multistability of plasma waves is investigated. Stable oscillation of plasma waves is also presented in dissipative plasmas. The book is meant for undergraduate and postgraduate students studying plasma physics. It will also serve a reference to the researchers, scientists and faculties to pursue the dynamics of nonlinear waves and its properties in plasmas. It describes the concept of dynamical systems and is useful in understanding exciting features, such as solitary wave, periodic wave, supernonlinear wave, chaotic, quasiperiodic and coexisting structures of nonlinear waves in plasmas. The concepts and approaches, discussed in the book, will also help the students and professionals to study such features in other nonlinear media.

Handbook of Dynamical Systems

Handbook of Dynamical Systems
Author: B. Hasselblatt,A. Katok
Publsiher: North Holland
Total Pages: 1232
Release: 2002-09-03
ISBN 10: 9780444826695
ISBN 13: 0444826696
Language: EN, FR, DE, ES & NL

Handbook of Dynamical Systems Book Review:

Volumes 1A and 1B. These volumes give a comprehensive survey of dynamics written by specialists in the various subfields of dynamical systems. The presentation attains coherence through a major introductory survey by the editors that organizes the entire subject, and by ample cross-references between individual surveys. The volumes are a valuable resource for dynamicists seeking to acquaint themselves with other specialties in the field, and to mathematicians active in other branches of mathematics who wish to learn about contemporary ideas and results dynamics. Assuming only general mathematical knowledge the surveys lead the reader towards the current state of research in dynamics. Volume 1B will appear 2005.

Stability of Dynamical Systems

Stability of Dynamical Systems
Author: Xiaoxin Liao,L.Q. Wang,P. Yu
Publsiher: Elsevier
Total Pages: 718
Release: 2007-08-01
ISBN 10: 9780080550619
ISBN 13: 0080550614
Language: EN, FR, DE, ES & NL

Stability of Dynamical Systems Book Review:

The main purpose of developing stability theory is to examine dynamic responses of a system to disturbances as the time approaches infinity. It has been and still is the object of intense investigations due to its intrinsic interest and its relevance to all practical systems in engineering, finance, natural science and social science. This monograph provides some state-of-the-art expositions of major advances in fundamental stability theories and methods for dynamic systems of ODE and DDE types and in limit cycle, normal form and Hopf bifurcation control of nonlinear dynamic systems. Presents comprehensive theory and methodology of stability analysis Can be used as textbook for graduate students in applied mathematics, mechanics, control theory, theoretical physics, mathematical biology, information theory, scientific computation Serves as a comprehensive handbook of stability theory for practicing aerospace, control, mechanical, structural, naval and civil engineers