Attractors Bifurcations And Chaos

Author : Tönu Puu
Publisher : Springer Science & Business Media
ISBN 13 : 3662040948
Total Pages : 513 pages
Book Rating : 4.42/5 ( download)

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Download or read book Attractors, Bifurcations, and Chaos written by Tönu Puu and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Attractors, Bifurcations, & Chaos - now in its second edition - begins with an introduction to mathematical methods in modern nonlinear dynamics and deals with differential equations. Phenomena such as bifurcations and deterministic chaos are given considerable emphasis, both in the methodological part, and in the second part, containing various applications in economics and in regional science. Coexistence of attractors and the multiplicity of development paths in nonlinear systems are central topics. The applications focus on issues such as business cycles, oligopoly, interregional trade dynamics, and economic development theory.

Author : Tönu Puu
Publisher : Springer Science & Business Media
ISBN 13 : 3540246991
Total Pages : 556 pages
Book Rating : 4.92/5 ( download)

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Download or read book Attractors, Bifurcations, & Chaos written by Tönu Puu and published by Springer Science & Business Media. This book was released on 2013-03-19 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: Attractors, Bifurcations, & Chaos - now in its second edition - begins with an introduction to mathematical methods in modern nonlinear dynamics and deals with differential equations. Phenomena such as bifurcations and deterministic chaos are given considerable emphasis, both in the methodological part, and in the second part, containing various applications in economics and in regional science. Coexistence of attractors and the multiplicity of development paths in nonlinear systems are central topics. The applications focus on issues such as business cycles, oligopoly, interregional trade dynamics, and economic development theory.

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 : Soumitro Banerjee
Publisher : Wiley-IEEE Press
ISBN 13 :
Total Pages : 480 pages
Book Rating : 4.56/5 ( download)

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Download or read book Nonlinear Phenomena in Power Electronics written by Soumitro Banerjee and published by Wiley-IEEE Press. This book was released on 2001-07-16 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Brings the knowledge of 24 experts in this maturing field out from the narrow confines of academic circles, and makes it accessible to graduate students and power electronics professionals alike. * Provides practicing engineers with the knowledge to predict power requirement behavior. * The insights gained from this all-inclusive compilation will ultimately lead to better design methodologies.

Author : Stephen Wiggins
Publisher : Springer Science & Business Media
ISBN 13 : 1461210429
Total Pages : 505 pages
Book Rating : 4.29/5 ( download)

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Download or read book Global Bifurcations and Chaos written by Stephen Wiggins and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: Global Bifurcations and Chaos: Analytical Methods is unique in the literature of chaos in that it not only defines the concept of chaos in deterministic systems, but it describes the mechanisms which give rise to chaos (i.e., homoclinic and heteroclinic motions) and derives explicit techniques whereby these mechanisms can be detected in specific systems. These techniques can be viewed as generalizations of Melnikov's method to multi-degree of freedom systems subject to slowly varying parameters and quasiperiodic excitations. A unique feature of the book is that each theorem is illustrated with drawings that enable the reader to build visual pictures of global dynamcis of the systems being described. This approach leads to an enhanced intuitive understanding of the theory.

Author : Wanda Szemplinska-Stupnicka
Publisher : World Scientific
ISBN 13 : 981448363X
Total Pages : 116 pages
Book Rating : 4.36/5 ( download)

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Download or read book Chaos, Bifurcations and Fractals Around Us written by Wanda Szemplinska-Stupnicka and published by World Scientific. This book was released on 2003-11-11 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last twenty years, a large number of books on nonlinear chaotic dynamics in deterministic dynamical systems have appeared. These academic tomes are intended for graduate students and require a deep knowledge of comprehensive, advanced mathematics. There is a need for a book that is accessible to general readers, a book that makes it possible to get a good deal of knowledge about complex chaotic phenomena in nonlinear oscillators without deep mathematical study. Chaos, Bifurcations and Fractals Around Us: A Brief Introduction fills that gap. It is a very short monograph that, owing to geometric interpretation complete with computer color graphics, makes it easy to understand even very complex advanced concepts of chaotic dynamics. This invaluable publication is also addressed to lecturers in engineering departments who want to include selected nonlinear problems in full time courses on general mechanics, vibrations or physics so as to encourage their students to conduct further study. Contents:Ueda's “Strange Attractors”PendulumVibrating System with Two Minima of Potential Energy Readership: Undergraduates, graduate students, academics and researchers in engineering. Keywords:Nonlinear Dynamics;Chaotic Vibrations;Nonlinear Resonance;Local and Global Bifurcations;Fractal Basins of Attraction;Transient Chaos;Persistent Chaos

Author : Jacob Palis Júnior
Publisher : Cambridge University Press
ISBN 13 : 9780521475723
Total Pages : 248 pages
Book Rating : 4.24/5 ( download)

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Download or read book Hyperbolicity and Sensitive Chaotic Dynamics at Homoclinic Bifurcations written by Jacob Palis Júnior and published by Cambridge University Press. This book was released on 1995-01-05 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introduction to the classical theory and its generalizations, aimed at mathematicians and scientists working in dynamical systems.

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 : Jan Awrejcewicz
Publisher : World Scientific
ISBN 13 : 9812384596
Total Pages : 564 pages
Book Rating : 4.91/5 ( download)

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Download or read book Bifurcation and Chaos in Nonsmooth Mechanical Systems written by Jan Awrejcewicz and published by World Scientific. This book was released on 2003 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the theoretical frame for studying lumped nonsmooth dynamical systems: the mathematical methods are recalled, and adapted numerical methods are introduced (differential inclusions, maximal monotone operators, Filippov theory, Aizerman theory, etc.). Tools available for the analysis of classical smooth nonlinear dynamics (stability analysis, the Melnikov method, bifurcation scenarios, numerical integrators, solvers, etc.) are extended to the nonsmooth frame. Many models and applications arising from mechanical engineering, electrical circuits, material behavior and civil engineering are investigated to illustrate theoretical and computational developments.

Author : David P. Feldman
Publisher : Princeton University Press
ISBN 13 : 0691161526
Total Pages : 262 pages
Book Rating : 4.25/5 ( download)

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Download or read book Chaos and Dynamical Systems written by David P. Feldman and published by Princeton University Press. This book was released on 2019-08-06 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaos and Dynamical Systems presents an accessible, clear introduction to dynamical systems and chaos theory, important and exciting areas that have shaped many scientific fields. While the rules governing dynamical systems are well-specified and simple, the behavior of many dynamical systems is remarkably complex. Of particular note, simple deterministic dynamical systems produce output that appears random and for which long-term prediction is impossible. Using little math beyond basic algebra, David Feldman gives readers a grounded, concrete, and concise overview. In initial chapters, Feldman introduces iterated functions and differential equations. He then surveys the key concepts and results to emerge from dynamical systems: chaos and the butterfly effect, deterministic randomness, bifurcations, universality, phase space, and strange attractors. Throughout, Feldman examines possible scientific implications of these phenomena for the study of complex systems, highlighting the relationships between simplicity and complexity, order and disorder. Filling the gap between popular accounts of dynamical systems and chaos and textbooks aimed at physicists and mathematicians, Chaos and Dynamical Systems will be highly useful not only to students at the undergraduate and advanced levels, but also to researchers in the natural, social, and biological sciences.