Global Bifurcations And Chaos

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 : Stephen Wiggins
Publisher :
ISBN 13 : 9781461210436
Total Pages : 514 pages
Book Rating : 4.37/5 ( download)

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Download or read book Global Bifurcations and Chaos written by Stephen Wiggins and published by . This book was released on 2014-09-01 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Wei-Bin Zhang
Publisher : World Scientific
ISBN 13 : 9812563334
Total Pages : 512 pages
Book Rating : 4.30/5 ( download)

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Download or read book Differential Equations, Bifurcations, and Chaos in Economics written by Wei-Bin Zhang and published by World Scientific. This book was released on 2005 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although the application of differential equations to economics is a vast and vibrant area, the subject has not been systematically studied; it is often treated as a subsidiary part of mathematical economics textbooks. This book aims to fill that void by providing a unique blend of the theory of differential equations and their exciting applications to dynamic economics. Containing not just a comprehensive introduction to the applications of the theory of linear (and linearized) differential equations to economic analysis, the book also studies nonlinear dynamical systems, which have only been widely applied to economic analysis in recent years. It provides comprehensive coverage of the most important concepts and theorems in the theory of differential equations in a way that can be understood by any reader who has a basic knowledge of calculus and linear algebra. In addition to traditional applications of the theory to economic dynamics, the book includes many recent developments in different fields of economics.

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 : 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 : Wei-Bin Zhang
Publisher : Elsevier
ISBN 13 : 0080462464
Total Pages : 459 pages
Book Rating : 4.62/5 ( download)

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Download or read book Discrete Dynamical Systems, Bifurcations and Chaos in Economics written by Wei-Bin Zhang and published by Elsevier. This book was released on 2006-01-05 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a unique blend of difference equations theory and its exciting applications to economics. It deals with not only theory of linear (and linearized) difference equations, but also nonlinear dynamical systems which have been widely applied to economic analysis in recent years. It studies most important concepts and theorems in difference equations theory in a way that can be understood by anyone who has basic knowledge of calculus and linear algebra. It contains well-known applications and many recent developments in different fields of economics. The book also simulates many models to illustrate paths of economic dynamics. A unique book concentrated on theory of discrete dynamical systems and its traditional as well as advanced applications to economics Mathematical definitions and theorems are introduced in a systematic and easily accessible way Examples are from almost all fields of economics; technically proceeding from basic to advanced topics Lively illustrations with numerous figures Numerous simulation to see paths of economic dynamics Comprehensive treatment of the subject with a comprehensive and easily accessible approach

Author : John Guckenheimer
Publisher : Springer Science & Business Media
ISBN 13 : 1461211409
Total Pages : 475 pages
Book Rating : 4.02/5 ( download)

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Download or read book Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields written by John Guckenheimer and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Wanda Szempli
Publisher : World Scientific
ISBN 13 : 9812386890
Total Pages : 117 pages
Book Rating : 4.92/5 ( download)

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Download or read book Chaos Bifurcations and Fractals Around Us written by Wanda Szempli and published by World Scientific. This book was released on 2003 with total page 117 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.

Author : Dirk Roose
Publisher : Springer Science & Business Media
ISBN 13 : 9400906595
Total Pages : 415 pages
Book Rating : 4.94/5 ( download)

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Download or read book Continuation and Bifurcations: Numerical Techniques and Applications written by Dirk Roose and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Research Workshop, Leuven, Belgium, September 18-22, 1989

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.