The Lorenz Equations

Author : Colin Sparrow
Publisher : Springer Science & Business Media
ISBN 13 : 1461257670
Total Pages : 280 pages
Book Rating : 4.77/5 ( download)

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Download or read book The Lorenz Equations written by Colin Sparrow and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: The equations which we are going to study in these notes were first presented in 1963 by E. N. Lorenz. They define a three-dimensional system of ordinary differential equations that depends on three real positive parameters. As we vary the parameters, we change the behaviour of the flow determined by the equations. For some parameter values, numerically computed solutions of the equations oscillate, apparently forever, in the pseudo-random way we now call "chaotic"; this is the main reason for the immense amount of interest generated by the equations in the eighteen years since Lorenz first presented them. In addition, there are some parameter values for which we see "preturbulence", a phenomenon in which trajectories oscillate chaotically for long periods of time before finally settling down to stable stationary or stable periodic behaviour, others in which we see "intermittent chaos", where trajectories alternate be tween chaotic and apparently stable periodic behaviours, and yet others in which we see "noisy periodicity", where trajectories appear chaotic though they stay very close to a non-stable periodic orbit. Though the Lorenz equations were not much studied in the years be tween 1963 and 1975, the number of man, woman, and computer hours spent on them in recent years - since they came to the general attention of mathematicians and other researchers - must be truly immense.

Author : Cleve B. Moler
Publisher : SIAM
ISBN 13 : 0898716608
Total Pages : 340 pages
Book Rating : 4.03/5 ( download)

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Download or read book Numerical Computing with MATLAB written by Cleve B. Moler and published by SIAM. This book was released on 2010-08-12 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: A revised textbook for introductory courses in numerical methods, MATLAB and technical computing, which emphasises the use of mathematical software.

Author : Flavio Lorenzelli
Publisher : CRC Press
ISBN 13 : 0203214587
Total Pages : 236 pages
Book Rating : 4.89/5 ( download)

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Download or read book The Essence Of Chaos written by Flavio Lorenzelli and published by CRC Press. This book was released on 2003-09-02 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Warwick Tucker
Publisher :
ISBN 13 : 9789150612967
Total Pages : 119 pages
Book Rating : 4.64/5 ( download)

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Download or read book The Lorenz Attractor Exists written by Warwick Tucker and published by . This book was released on 1998 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Steven H. Strogatz
Publisher : CRC Press
ISBN 13 : 0429961111
Total Pages : 532 pages
Book Rating : 4.13/5 ( download)

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Download or read book Nonlinear Dynamics and Chaos written by Steven H. Strogatz and published by CRC Press. This book was released on 2018-05-04 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : David D. Nolte
Publisher : Oxford University Press
ISBN 13 : 0192528505
Total Pages : 384 pages
Book Rating : 4.06/5 ( download)

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Download or read book Galileo Unbound written by David D. Nolte and published by Oxford University Press. This book was released on 2018-07-12 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.

Author : Morris W. Hirsch
Publisher : Academic Press
ISBN 13 : 0123497035
Total Pages : 433 pages
Book Rating : 4.31/5 ( download)

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Download or read book Differential Equations, Dynamical Systems, and an Introduction to Chaos written by Morris W. Hirsch and published by Academic Press. This book was released on 2004 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thirty years in the making, this revised text by three of the world's leading mathematicians covers the dynamical aspects of ordinary differential equations. it explores the relations between dynamical systems and certain fields outside pure mathematics, and has become the standard textbook for graduate courses in this area. The Second Edition now brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra. The authors are tops in the field of advanced mathematics, including Steve Smale who is a recipient of.

Author : Colin Sparrow
Publisher :
ISBN 13 : 9781461257684
Total Pages : 284 pages
Book Rating : 4.89/5 ( download)

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Download or read book The Lorenz Equations written by Colin Sparrow and published by . This book was released on 1982-12-01 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Steven L. Brunton
Publisher : Cambridge University Press
ISBN 13 : 1009098489
Total Pages : 615 pages
Book Rating : 4.89/5 ( download)

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Download or read book Data-Driven Science and Engineering written by Steven L. Brunton and published by Cambridge University Press. This book was released on 2022-05-05 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: A textbook covering data-science and machine learning methods for modelling and control in engineering and science, with Python and MATLAB®.

Author :
Publisher :
ISBN 13 : 9814468673
Total Pages : pages
Book Rating : 4.71/5 ( download)

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Download or read book Elegant Chaos written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: