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 : Richard Kautz
Editor : Oxford University Press
Release : 2010-11-04
File Download : 369 Pages
ISBN-10 : 9780199594580
Price : FREE

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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 : Flavio Lorenzelli
Editor : CRC Press
Release : 2003-09-02
File Download : 227 Pages
ISBN-10 : 9780203214589
Price : FREE

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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 : Kathleen Alligood
Editor : Springer
Release : 2012-12-06
File Download : 603 Pages
ISBN-10 : 9783642592812
Price : FREE

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This volume sets out the basic applied mathematical and numerical methods of chaotic dynamics and illustrates the wide range of phenomena, inside and outside the laboratory, that can be treated as chaotic processes. Originally published in 1986. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

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Genre Book : Science
Author : Arun V. Holden
Editor : Princeton University Press
Release : 2014-07-14
File Download : 334 Pages
ISBN-10 : 9781400858156
Price : FREE

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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 : James Gleick
Editor : Open Road Media
Release : 2011-03-22
File Download : 360 Pages
ISBN-10 : 9781453210475
Price : FREE

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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 : John H. Holland
Editor : OUP Oxford
Release : 2000
File Download : 258 Pages
ISBN-10 : 0192862111
Price : FREE

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A journalist's twenty-year fascination with the Manson murders leads to shocking new revelations about the FBI's involvement in this riveting reassessment of an infamous case in American history. Over two grim nights in Los Angeles, the young followers of Charles Manson murdered seven people, including the actress Sharon Tate, then eight months pregnant. With no mercy and seemingly no motive, the Manson Family followed their leader's every order -- their crimes lit a flame of paranoia across the nation, spelling the end of the sixties. Manson became one of history's most infamous criminals, his name forever attached to an era when charlatans mixed with prodigies, free love was as possible as brainwashing, and utopia -- or dystopia -- was just an acid trip away. Twenty years ago, when journalist Tom O'Neill was reporting a magazine piece about the murders, he worried there was nothing new to say. Then he unearthed shocking evidence of a cover-up behind the "official" story, including police carelessness, legal misconduct, and potential surveillance by intelligence agents. When a tense interview with Vincent Bugliosi -- prosecutor of the Manson Family and author of Helter Skelter -- turned a friendly source into a nemesis, O'Neill knew he was onto something. But every discovery brought more questions: Who were Manson's real friends in Hollywood, and how far would they go to hide their ties? Why didn't law enforcement, including Manson's own parole officer, act on their many chances to stop him? And how did Manson -- an illiterate ex-con -- turn a group of peaceful hippies into remorseless killers? O'Neill's quest for the truth led him from reclusive celebrities to seasoned spies, from San Francisco's summer of love to the shadowy sites of the CIA's mind-control experiments, on a trail rife with shady cover-ups and suspicious coincidences. The product of two decades of reporting, hundreds of new interviews, and dozens of never-before-seen documents from the LAPD, the FBI, and the CIA, Chaos mounts an argument that could be, according to Los Angeles Deputy District Attorney Steven Kay, strong enough to overturn the verdicts on the Manson murders. This is a book that overturns our understanding of a pivotal time in American history.

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Genre Book : True Crime
Author : Tom O'Neill
Editor : Little, Brown
Release : 2019-06-25
File Download : 528 Pages
ISBN-10 : 9780316477574
Price : FREE

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Presents an introduction to chaos theory.

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

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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 : Kevin Judd
Editor : Springer Science & Business Media
Release : 1997-12
File Download : 333 Pages
ISBN-10 : 0817638679
Price : FREE

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Based on courses given at the universities of Texas and California, this book treats an active field of research that touches upon the foundations of physics and chemistry. It presents, in as simple a manner as possible, the basic mechanisms that determine the dynamical evolution of both classical and quantum systems in sufficient generality to include quantum phenomena. The book begins with a discussion of Noether's theorem, integrability, KAM theory, and a definition of chaotic behavior; continues with a detailed discussion of area-preserving maps, integrable quantum systems, spectral properties, path integrals, and periodically driven systems; and concludes by showing how to apply the ideas to stochastic systems. The presentation is complete and self-contained; appendices provide much of the needed mathematical background, and there are extensive references to the current literature; while problems at the ends of chapters help students clarify their understanding. This new edition has an updated presentation throughout, and a new chapter on open quantum systems.

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Genre Book : Science
Author : Linda Reichl
Editor : Springer Science & Business Media
Release : 2013-11-11
File Download : 675 Pages
ISBN-10 : 9781475743500
Price : FREE

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