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Chaos: The Science of Predictable Random Motion bridges the gap between introductions for the layman and college-level texts with an account of chaos theory based on elementary mathematics. It develops the science of dynamics in terms of small time steps, describes the phenomenon of chaos through simple examples, and concludes with a close look at a homoclinic tangle, the mathematical monster at the heart of chaos. The presentation is enhanced by numerousfigures, animations of chaotic motion (available on a companion CD), and biographical sketches of the pioneers of dynamics and chaos theory.

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Genre Book : Mathematics
Author Book : Richard Kautz
Publisher : Oxford University Press
Release Book : 2010-11-04
Download Book : 369 Pages
ISBN-10 : 9780199594580


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The study of chaotic systems has become a major scientific pursuit in recent years, shedding light on the apparently random behaviour observed in fields as diverse as climatology and mechanics. InThe Essence of Chaos Edward Lorenz, one of the founding fathers of Chaos and the originator of its seminal concept of the Butterfly Effect, presents his own landscape of our current understanding of the field. Lorenz presents everyday examples of chaotic behaviour, such as the toss of a coin, the pinball's path, the fall of a leaf, and explains in elementary mathematical strms how their essentially chaotic nature can be understood. His principal example involved the construction of a model of a board sliding down a ski slope. Through this model Lorenz illustrates chaotic phenomena and the related concepts of bifurcation and strange attractors. He also provides the context in which chaos can be related to the similarly emergent fields of nonlinearity, complexity and fractals. As an early pioneer of chaos, Lorenz also provides his own story of the human endeavour in developing this new field. He describes his initial encounters with chaos through his study of climate and introduces many of the personalities who contributed early breakthroughs. His seminal paper, "Does the Flap of a Butterfly's Wing in Brazil Set Off a Tornado in Texas?" is published for the first time.

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Genre Book : Science
Author Book : Flavio Lorenzelli
Publisher : CRC Press
Release Book : 2003-09-02
Download Book : 227 Pages
ISBN-10 : 9780203214589


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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.

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Genre Book : Mathematics
Author Book : Kathleen Alligood
Publisher : Springer
Release Book : 2012-12-06
Download Book : 603 Pages
ISBN-10 : 9783642592812


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We are confronted with emergent systems everywhere and Holland shows how a theory of emergence can predict many complex behaviours in art and science. This book will appeal to scientists and anyone interested in scientific theory.

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Genre Book : Mathematics
Author Book : John H. Holland
Publisher : OUP Oxford
Release Book : 2000
Download Book : 258 Pages
ISBN-10 : 0192862111


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The “highly entertaining” New York Times bestseller, which explains chaos theory and the butterfly effect, from the author of The Information (Chicago Tribune). For centuries, scientific thought was focused on bringing order to the natural world. But even as relativity and quantum mechanics undermined that rigid certainty in the first half of the twentieth century, the scientific community clung to the idea that any system, no matter how complex, could be reduced to a simple pattern. In the 1960s, a small group of radical thinkers began to take that notion apart, placing new importance on the tiny experimental irregularities that scientists had long learned to ignore. Miniscule differences in data, they said, would eventually produce massive ones—and complex systems like the weather, economics, and human behavior suddenly became clearer and more beautiful than they had ever been before. In this seminal work of scientific writing, James Gleick lays out a cutting edge field of science with enough grace and precision that any reader will be able to grasp the science behind the beautiful complexity of the world around us. With more than a million copies sold, Chaos is “a groundbreaking book about what seems to be the future of physics” by a writer who has been a finalist for both the Pulitzer Prize and the National Book Award, the author of Time Travel: A History and Genius: The Life and Science of Richard Feynman (Publishers Weekly).

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Genre Book : Science
Author Book : James Gleick
Publisher : Open Road Media
Release Book : 2011-03-22
Download Book : 360 Pages
ISBN-10 : 9781453210475


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Presents an introduction to chaos theory.

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Genre Book : Mathematics
Author Book : John Banks
Publisher : Cambridge University Press
Release Book : 2003-05-08
Download Book : 294 Pages
ISBN-10 : 0521531047


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The articles in this Control and Chaos volume are an outgrowth of a US-Australia workshop held in Hawaii in 1995. Experts in dynamical systems theory and control theory from the US and Australia, as well as England and Japan, focused on the problem of controlling nonlinear and potentially chaotic systems using limited control effort. The formal contributions take into account the discussions and commentaries of the participants and are reflected at the end of each article. Part I contains papers dealing with modeling, behavior, reconstruction, prediction and numerics. Part II deals with controlling complex systems by means of embedding unstable periodic orbits, targeting, filtering, optimization and adaptive methods. Part III contains four applications papers including the control of a bouncing ball, evolutionary stability, chaos in ecosystems, and neural networks. Contents and Contributors: Understanding Complex Dynamics Triangulating Noisy Dynamical Systems S. Allie, A. Mees, K. Judd, D. Watson Attractor Reconstruction and Control Using Interspike Intervals T. Sauer Modeling Chaos from Experimental Data K. Judd, A. Mees Chaos in Symplectic Discretization of the Pendulum and Sine-Gordon Equations B.M. Herbst, C.M. Schober Collapsing Effects in Computation of Dynamical Systems P. Diamond, P. Kloeden, A. Pokrovskii Bifurications in the Falkner-Skan equation C. Sparrow Some Characterizations of Low-dimensional Dynamical Systems with Time-reversal Symmetry J.A.G. Roberts Controlling Complex Systems Control of Chaos by Means of Embedded Unstable Periodic Orbits E. Ott, B.R. Hunt Notch Filter Feedback Control for k-Period Motion in a Chaotic System W.J. Grantham, A.M. Athalye Targeting and Control of Chaos E.J. Kostelich, E. Barreto Adaptive Nonlinear Control: A Lyapunov Approach P.V. Kokotovic, M. Krstic Creating and Targeting Periodic Orbits K. Glass, M. Renton, K. Judd, A. Mees Dynamical Systems, Optimization, and Chaos J.B. Moore Combined Controls for Noisy Chaotic Systems M. Paskota, K.L. Teo, A. Mees Complex Dynamics in Adaptive Systems I.M.Y. Mareels Hitting Times to a Target for the Baker's Map A. Mazer Applications Controllable Targets Near a Chaotic Attractor T.L. Vincent The Dynamics of Evolutionary Stable Strategies Y. Cohen, T.L. Vincent Nitrogen Cycling and the Control of Chaos in a Boreal Forest Model J. Pastor, Y. Cohen Self-organization Dynamics in Chaotic Neural Networks M. Watanabe, K. Aihara, S. Kondo Series: Mathematical Modeling, Volume 8

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Genre Book : Language Arts & Disciplines
Author Book : Kevin Judd
Publisher : Springer Science & Business Media
Release Book : 1997-12
Download Book : 333 Pages
ISBN-10 : 0817638679


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Chaos and Nonlinear Dynamics introduces students, scientists, and engineers to the full range of activity in the rapidly growing field on nonlinear dynamics. Using a step-by-step introduction to dynamics and geometry in state space as the central focus of understanding nonlinear dynamics, thisbook includes a thorough treatment of both differential equation models and iterated map models (including a derivation of the famous Feigenbaum numbers). It is the only book at this level to include the increasingly important field of pattern formation and a survey of the controversial questions ofquantum chaos. Important tools such as Lyapunov exponents and fractal dimensions are treated in detail. With over 200 figures and diagrams, and analytic and computer exercises for every chapter, the book can be used as a course-text or for self-instruction. This second edition has been restructuredto make the book even more useful as a course text:many of the more complex examples and derivations have been moved to appendices. The extensive collection of annotated references has been updated through January 2000 and now includes listings of World Wide Web sites at many of the major nonlineardynamics research centers. From reviews on the 1/e: 'What has been lacking is a single book that takes the reader with nothing but a knowledge of elementary calculus and physics all the way to the frontiers of research in chaos and nonlinear dynamics in all its facets. [...] a serious student,teacher, or researcher would be delighted to have this book on the shelf as a reference and as a window to the literature in this exciting and rapidly growing new field of chaos.' J.C. Sprott, American Journal of Physics, September 19944 'I congratulate the author on having managed to write anextremely thorough, comprehensive, and entertaining introduction to the fascinating field of nonlinear dynamics. His book is highly self- explanatory and ideally suited for self-instruction. There is hardly any question that the author does not address in an exceptionally readable manner. [...] Istrongly recommend it to those looking for a comprehensive, practical, and not highly mathematical approach to the subject.' E.A. Hunt, IEEE Spectrum, December 1994

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Genre Book : Mathematics
Author Book : Robert C. Hilborn
Publisher : Oxford University Press on Demand
Release Book : 2000
Download Book : 650 Pages
ISBN-10 : 0198507232


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Chaos control refers to purposefully manipulating chaotic dynamical behaviors of some complex nonlinear systems. There exists no similar control theory-oriented book available in the market that is devoted to the subject of chaos control, written by control engineers for control engineers. World-renowned leading experts in the field provide their state-of-the-art survey about the extensive research that has been done over the last few years in this subject. The new technology of chaos control has major impact on novel engineering applications such as telecommunications, power systems, liquid mixing, internet technology, high-performance circuits and devices, biological systems modeling like the brain and the heart, and decision making. The book is not only aimed at active researchers in the field of chaos control involving control and systems engineers, theoretical and experimental physicists, and applied mathematicians, but also at a general audience in related fields.

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Genre Book : Technology & Engineering
Author Book : Guanrong Chen
Publisher : Springer Science & Business Media
Release Book : 2003-07-25
Download Book : 374 Pages
ISBN-10 : 3540404058


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Chaos is a fascinating phenomenon that has been observed in nature, laboratory, and has been applied in various real-world applications. Chaotic systems are deterministic with no random elements involved yet their behavior appears to be random. Obser- tions of chaotic behavior in nature include weather and climate, the dynamics of sat- lites in the solar system, the time evolution of the magnetic field of celestial bodies, population growth in ecology, to mention only a few examples. Chaos has been observed in the laboratory in a number of systems such as electrical circuits, lasers, chemical reactions, fluid dynamics, mechanical systems, and magneto-mechanical devices. Chaotic behavior has also found numerous applications in electrical and communication engineering, information and communication technologies, biology and medicine. To the best of our knowledge, this is the first book edited on chaos applications in intelligent computing. To access the latest research related to chaos applications in intelligent computing, we launched the book project where researchers from all over the world provide the necessary coverage of the mentioned field. The primary obj- tive of this project was to assemble as much research coverage as possible related to the field by defining the latest innovative technologies and providing the most c- prehensive list of research references.

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Genre Book : Mathematics
Author Book : Ljupco Kocarev
Publisher : Springer Science & Business Media
Release Book : 2009-06-09
Download Book : 380 Pages
ISBN-10 : 9783540959717