[PDF] Nonlinearity Bifurcation And Chaos eBook

Author : Steven H. Strogatz
Publisher : CRC Press
Page : 532 pages
File Size : 15,6 MB
Release : 2018-05-04
Category : Mathematics
ISBN : 0429961111

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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 : BoD – Books on Demand
Page : 360 pages
File Size : 31,86 MB
Release : 2012-10-24
Category : Mathematics
ISBN : 9535108166

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Nonlinearity, Bifurcation and Chaos - Theory and Application is an edited book focused on introducing both theoretical and application oriented approaches in science and engineering. It contains 12 chapters, and is recommended for university teachers, scientists, researchers, engineers, as well as graduate and post-graduate students either working or interested in the field of nonlinearity, bifurcation and chaos.

Author : Tönu Puu
Publisher : Springer Science & Business Media
Page : 572 pages
File Size : 13,48 MB
Release : 2003-07-10
Category : Mathematics
ISBN : 9783540402268

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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 : Wanda Szemplinska-stupnicka
Publisher : World Scientific
Page : 117 pages
File Size : 48,10 MB
Release : 2003-11-11
Category : Technology & Engineering
ISBN : 981448363X

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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.

Author : Jan Awrejcewicz
Publisher : World Scientific
Page : 564 pages
File Size : 33,49 MB
Release : 2003
Category : Science
ISBN : 9812384596

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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 : Tönu Puu
Publisher : Springer Science & Business Media
Page : 513 pages
File Size : 10,65 MB
Release : 2013-04-17
Category : Business & Economics
ISBN : 3662040948

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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 : John Guckenheimer
Publisher : Springer Science & Business Media
Page : 475 pages
File Size : 25,24 MB
Release : 2013-11-21
Category : Mathematics
ISBN : 1461211409

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An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved.

Author : Frank Scott
Publisher : States Academic Press
Page : 248 pages
File Size : 32,96 MB
Release : 2021-11-16
Category : Mathematics
ISBN : 9781639891825

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The three common features exhibited by both natural and technological processes are nonlinearity, bifurcation and chaos theory. Floquet exponents and bifurcations in switched converters, dynamics of a pendulum of variable length, mathematical modeling, and non-linearity in structural dynamics are some of the significant concepts in this area of study. The mathematical study of changes in the qualitative structure of a given family and solutions of family of differential equations is referred as bifurcation theory. The branch of mathematics which deals with the study of chaos in dynamical systems where the irregularities and random states of disorder are governed by underlying patterns and deterministic laws is termed as chaos theory. The book presents researches and studies performed by experts across the globe. It includes some of the vital pieces of work being conducted across the world, on various topics related to essential elements of nonlinearity, bifurcation and chaos theory. This book is a resource guide for experts as well as students.

Author : Muthusamy Lakshmanan
Publisher : World Scientific
Page : 346 pages
File Size : 42,96 MB
Release : 1996
Category : Science
ISBN : 9789810221430

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This book deals with the bifurcation and chaotic aspects of damped and driven nonlinear oscillators. The analytical and numerical aspects of the chaotic dynamics of these oscillators are covered, together with appropriate experimental studies using nonlinear electronic circuits. Recent exciting developments in chaos research are also discussed, such as the control and synchronization of chaos and possible technological applications.

Author : Soumitro Banerjee
Publisher : Wiley-IEEE Press
Page : 480 pages
File Size : 33,52 MB
Release : 2001-07-16
Category : Mathematics
ISBN :

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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.