The Illustrated Dictionary of Nonlinear Dynamics and Chaos

The Illustrated Dictionary of Nonlinear Dynamics and Chaos

Author: Tomasz Kapitaniak

Publisher:

Published: 1999-03-03

Total Pages: 292

ISBN-13:

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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

Chaos and Nonlinear Dynamics

Author: Robert C. Hilborn

Publisher:

Published: 2000

Total Pages: 676

ISBN-13: 9780198507239

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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

Nonlinear Dynamics and Chaos

Author: J. M. T. Thompson

Publisher: John Wiley & Sons

Published: 2002-02-15

Total Pages: 492

ISBN-13: 9780471876847

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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

CRC Concise Encyclopedia of Mathematics

Author: Eric W. Weisstein

Publisher: CRC Press

Published: 2002-12-12

Total Pages: 3253

ISBN-13: 1420035223

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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


BIOMAT 2012

BIOMAT 2012

Author: Rubem P. Mondaini

Publisher: World Scientific

Published: 2013

Total Pages: 406

ISBN-13: 9814520829

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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.


A Smooth and Discontinuous Oscillator

A Smooth and Discontinuous Oscillator

Author: Qingjie Cao

Publisher: Springer

Published: 2016-09-27

Total Pages: 273

ISBN-13: 3662530945

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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.


Action and Reaction in the World System

Action and Reaction in the World System

Author: Thierry de Montbrial

Publisher: UBC Press

Published: 2013-01-25

Total Pages: 377

ISBN-13: 0774824743

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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.


The Duffing Equation

The Duffing Equation

Author: Ivana Kovacic

Publisher: John Wiley & Sons

Published: 2011-02-11

Total Pages: 335

ISBN-13: 0470977833

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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.


The Chaotic Pendulum

The Chaotic Pendulum

Author: M. Gitterman

Publisher: World Scientific

Published: 2010

Total Pages: 157

ISBN-13: 9814322008

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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.