The Illustrated Dictionary Of Nonlinear Dynamics And Chaos

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The Illustrated Dictionary of Nonlinear Dynamics and Chaos

Author : Tomasz Kapitaniak,Steven R. Bishop
Publisher : Unknown
Page : 292 pages
File Size : 40,7 Mb
Release : 1999-03-03
Category : Mathematics
ISBN : STANFORD:36105028488976

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The Illustrated Dictionary of Nonlinear Dynamics and Chaos by Tomasz Kapitaniak,Steven R. Bishop Pdf

The study of nonlinear dynamics is one of the most active fields in modern science. It reaches across the whole range of scientific study, and is applied in fields as diverse as physics, engineering, biology, economics and medicine. However, the mathematical language used to describe nonlinear dynamics, and the proliferation of new terminology, can make the use of nonlinear dynamics a daunting task to the non-specialist. In addition,the simultaneous growth in the use of nonlinear dynamics across different fields, and the cross-fertilization of ideas from different disciplines, mean that names and methods used and developed in one field may be altered when 're-discovered' in a different context, making understanding the literature a difficult and time-consuming task. The Illustrated Dictionary of Nonlinear Dynamics and Chaos addresses these problems. It presents, in an alphabetical format, the key terms, theorems and equations which arise in the study of nonlinear dynamics. New mathematical ideas are described and explained with examples and, where appropriate, illustrations are included to aid clarification and understanding. For some entries, the descriptions are self-contained, but should more detail be required, references are included for further reading. Where alternative terms are used for a single concept, an entry is placed under the name in most common usage, with cross-references given under other names. The Illustrated Dictionary of Nonlinear Dynamics and Chaos is an invaluable reference source for all those who use nonlinear dynamics in their research, whether they are newcomers to the field who need help to understand the literature, or more experienced researchers who need a concise and handy reference.

Chaos and Nonlinear Dynamics

Author : Robert C. Hilborn
Publisher : Unknown
Page : 676 pages
File Size : 55,8 Mb
Release : 2000
Category : Mathematics
ISBN : 0198507232

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Chaos and Nonlinear Dynamics by Robert C. Hilborn Pdf

This book introduces readers to the full range of current and background activity in the rapidly growing field of nonlinear dynamics. It uses a step-by-step introduction to dynamics and geometry in state space to help in understanding nonlinear dynamics and includes a thorough treatment of both differential equation models and iterated map models as well as a derivation of the famous Feigenbaum numbers. It is the only introductory book available that includes the important field of pattern formation and a survey of the controversial questions of quantum chaos. This second edition has been restructured for easier use and the extensive annotated references are updated through January 2000 and include many web sites for a number of the major nonlinear dynamics research centers. With over 200 figures and diagrams, analytic and computer exercises this book is a necessity for both the classroom and the lab.

Nonlinear Dynamics and Chaos

Author : J. M. T. Thompson,H. B. Stewart
Publisher : John Wiley & Sons
Page : 492 pages
File Size : 51,6 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.

CRC Concise Encyclopedia of Mathematics

Author : Eric W. Weisstein
Publisher : CRC Press
Page : 3253 pages
File Size : 52,6 Mb
Release : 2002-12-12
Category : Mathematics
ISBN : 9781420035223

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CRC Concise Encyclopedia of Mathematics by Eric W. Weisstein Pdf

Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d

Nonlinear Dynamics and Chaos

Author : Steven H. Strogatz
Publisher : CRC Press
Page : 532 pages
File Size : 41,5 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.

A Smooth and Discontinuous Oscillator

Author : Qingjie Cao,Alain Léger
Publisher : Springer
Page : 262 pages
File Size : 55,6 Mb
Release : 2016-09-27
Category : Technology & Engineering
ISBN : 9783662530948

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A Smooth and Discontinuous Oscillator by Qingjie Cao,Alain Léger Pdf

This is the first book to introduce the irrational elliptic function series, providing a theoretical treatment for the smooth and discontinuous system and opening a new branch of applied mathematics. The discovery of the smooth and discontinuous (SD) oscillator and the SD attractors discussed in this book represents a further milestone in nonlinear dynamics, following on the discovery of the Ueda attractor in 1961 and Lorenz attractor in 1963. This particular system bears significant similarities to the Duffing oscillator, exhibiting the standard dynamics governed by the hyperbolic structure associated with the stationary state of the double well. However, there is a substantial departure in nonlinear dynamics from standard dynamics at the discontinuous stage. The constructed irrational elliptic function series, which offers a way to directly approach the nature dynamics analytically for both smooth and discontinuous behaviours including the unperturbed periodic motions and the perturbed chaotic attractors without any truncation, is of particular interest. Readers will also gain a deeper understanding of the actual nonlinear phenomena by means of a simple mechanical model: the theory, methodology, and the applications in various interlinked disciplines of sciences and engineering. This book offers a valuable resource for researchers, professionals and postgraduate students in mechanical engineering, non-linear dynamics, and related areas, such as nonlinear modelling in various fields of mathematics, physics and the engineering sciences.

The Duffing Equation

Author : Ivana Kovacic,Michael J. Brennan
Publisher : John Wiley & Sons
Page : 335 pages
File Size : 54,7 Mb
Release : 2011-02-11
Category : Science
ISBN : 9780470977835

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The Duffing Equation by Ivana Kovacic,Michael J. Brennan Pdf

The Duffing Equation: Nonlinear Oscillators and their Behaviour brings together the results of a wealth of disseminated research literature on the Duffing equation, a key engineering model with a vast number of applications in science and engineering, summarizing the findings of this research. Each chapter is written by an expert contributor in the field of nonlinear dynamics and addresses a different form of the equation, relating it to various oscillatory problems and clearly linking the problem with the mathematics that describe it. The editors and the contributors explain the mathematical techniques required to study nonlinear dynamics, helping the reader with little mathematical background to understand the text. The Duffing Equation provides a reference text for postgraduate and students and researchers of mechanical engineering and vibration / nonlinear dynamics as well as a useful tool for practising mechanical engineers. Includes a chapter devoted to historical background on Georg Duffing and the equation that was named after him. Includes a chapter solely devoted to practical examples of systems whose dynamic behaviour is described by the Duffing equation. Contains a comprehensive treatment of the various forms of the Duffing equation. Uses experimental, analytical and numerical methods as well as concepts of nonlinear dynamics to treat the physical systems in a unified way.

BIOMAT 2012

Author : Rubem P. Mondaini
Publisher : World Scientific
Page : 406 pages
File Size : 54,5 Mb
Release : 2013
Category : Mathematics
ISBN : 9789814520829

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BIOMAT 2012 by Rubem P. Mondaini Pdf

This is a book of a series on interdisciplinary topics of the Biological and Mathematical Sciences. The chapters correspond to selected papers on special research themes, which were presented at BIOMAT 2012 International Symposium on Mathematical and Computational Biology, in Tempe, Arizona, USA, November 6-10. This book contains state-of-the art articles on special research topics on mathematical biology, biological physics and mathematical modeling of biosystems; comprehensive reviews on interdisciplinary areas written by prominent leaders of scientific research groups. The treatment is both pedagogical and advanced in order to motivate research students as well as to fulfill the requirements of professional practitioners.

Complex Behavior of Switching Power Converters

Author : Chi Kong Tse
Publisher : CRC Press
Page : 279 pages
File Size : 45,6 Mb
Release : 2003-07-28
Category : Technology & Engineering
ISBN : 9780203494554

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Complex Behavior of Switching Power Converters by Chi Kong Tse Pdf

Power electronics is a discipline spawned by real-life applications in industrial, commercial, residential and aerospace environments. Much of its development evolves around some immediate need for solving specific power conversion problems. This comprehensive book focuses on the typical bifurcation scenarios and nonlinear behavior observed in swit

Nonlinear Dynamics and Chaos with Student Solutions Manual

Author : Steven H. Strogatz
Publisher : CRC Press
Page : 935 pages
File Size : 51,9 Mb
Release : 2018-09-21
Category : Mathematics
ISBN : 9780429680168

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Nonlinear Dynamics and Chaos with Student Solutions Manual 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.

Dissipative Solitons in Reaction Diffusion Systems

Author : Andreas Liehr
Publisher : Springer Science & Business Media
Page : 227 pages
File Size : 41,6 Mb
Release : 2013-03-27
Category : Science
ISBN : 9783642312519

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Dissipative Solitons in Reaction Diffusion Systems by Andreas Liehr Pdf

Why writing a book about a specialized task of the large topic of complex systems? And who will read it? The answer is simple: The fascination for a didactically valuable point of view, the elegance of a closed concept and the lack of a comprehensive disquisition. The fascinating part is that field equations can have localized solutions exhibiting the typical characteristics of particles. Regarding the field equations this book focuses on, the field phenomenon of localized solutions can be described in the context of a particle formalism, which leads to a set of ordinary differential equations covering the time evolution of the position and the velocity of each particle. Moreover, starting from these particle dynamics and making the transition to many body systems, one considers typical phenomena of many body systems as shock waves and phase transitions, which themselves can be described as field phenomena. Such transitions between different level of modelling are well known from conservative systems, where localized solutions of quantum field theory lead to the mechanisms of elementary particle interaction and from this to field equations describing the properties of matter. However, in dissipative systems such transitions have not been considered yet, which is adjusted by the presented book. The elegance of a closed concept starts with the observation of self-organized current filaments in a semiconductor gas discharge system. These filaments move on random paths and exhibit certain particle features like scattering or the formation of bound states. Neither the reasons for the propagation of the filaments nor the laws of the interaction between the filaments can be registered by direct observations. Therefore a model is established, which is phenomenological in the first instance due to the complexity of the experimental system. This model allows to understand the existence of localized structures, their mechanisms of movement, and their interaction, at least, on a qualitative level. But this model is also the starting point for developing a data analysis method that enables the detection of movement and interaction mechanisms of the investigated localized solutions. The topic is rounded of by applying the data analysis to real experimental data and comparing the experimental observations to the predictions of the model. A comprehensive publication covering the interesting topic of localized solutions in reaction diffusion systems in its width and its relation to the well known phenomena of spirals and patterns does not yet exist, and this is the third reason for writing this book. Although the book focuses on a specific experimental system the model equations are as simple as possible so that the discussed methods should be adaptable to a large class of systems showing particle-like structures. Therefore, this book should attract not only the experienced scientist, who is interested in self-organization phenomena, but also the student, who would like to understand the investigation of a complex system on the basis of a continuous description.

Action and Reaction in the World System

Author : Thierry de Montbrial
Publisher : UBC Press
Page : 377 pages
File Size : 52,6 Mb
Release : 2013-01-25
Category : Political Science
ISBN : 9780774824743

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Action and Reaction in the World System by Thierry de Montbrial Pdf

This book occupies the same niche as Raymond Aron’s 1962 classic, Peace and War. While Aron wrote during the Cold War, Thierry de Montbrial writes about the post-Soviet international system, a system that is multipolar, ideologically heterogeneous, and thus highly unstable. In this book, he lays the foundation for a praxeology, or a “science of action,” to facilitate a better understanding of the dynamics of international problems and a more systematic approach to policy making. A major contribution to international relations theory and winner of the 2002 Georges Pompidou Prize, this book offers the necessary keys to decrypt the international system in the 21st century.

Nonlinear Dynamics

Author : Muthusamy Lakshmanan,Shanmuganathan Rajaseekar
Publisher : Springer Science & Business Media
Page : 628 pages
File Size : 50,8 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.

Nonlinear Mechanics of Complex Structures

Author : Holm Altenbach,Marco Amabili,Yuri V. Mikhlin
Publisher : Springer Nature
Page : 476 pages
File Size : 54,6 Mb
Release : 2021-07-29
Category : Science
ISBN : 9783030758905

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Nonlinear Mechanics of Complex Structures by Holm Altenbach,Marco Amabili,Yuri V. Mikhlin Pdf

This book covers different topics of nonlinear mechanics in complex structures, such as the appearance of new nonlinear phenomena and the behavior of finite-dimensional and distributed nonlinear systems, including numerous systems directly connected with important technological problems.

The Chaotic Pendulum

Author : M. Gitterman
Publisher : World Scientific
Page : 157 pages
File Size : 43,6 Mb
Release : 2010
Category : Science
ISBN : 9789814322003

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The Chaotic Pendulum by M. Gitterman Pdf

The chaotic behavior of pendulum is usually associated with the random force acting on a pendulum (Brownian motion). This book presents a comprehensive description of these phenomena going on in underdamped and overdamped pendula subject to additive and multiplicative periodic and random forces.