Dynamics and bifurcations by Jack K. Hale

Cover of: Dynamics and bifurcations | Jack K. Hale

Published by Springer in New York .

Written in English

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Subjects:

  • Differential equations,
  • Differentiable dynamical systems,
  • Bifurcation theory

Edition Notes

Includes bibliographical references (p. [545]-558) and index.

Book details

StatementJack K. Hale, Hüseyin Koçak.
SeriesTexts in applied mathematics ;, 3
ContributionsKoçak, Hüseyin.
Classifications
LC ClassificationsQA372 .H183 1996
The Physical Object
Paginationxiv, 568 p. :
Number of Pages568
ID Numbers
Open LibraryOL727080M
ISBN 100387971416, 3540971416
LC Control Number97115633

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Get this from a library. Dynamics and bifurcations. [Jack K Hale; Hüseyin Koçak] -- Focuses on the subject of dynamical systems. The fundamental ideas of dynamics and bifurcations are explained. J.K. Hale, H. Kocak, and H. ButtanriDynamics and Bifurcations"This book takes the reader step by step through the vast subject of dynamical systems.

Proceeding from 1 to 2 dimensions and onto higher dimensions in separate self-contained sections, the text is mathematically rigorous yet Dynamics and bifurcations book.

In recent years, due primarily to the proliferation of computers, dynamical systems has again returned to its roots in applications. It is the aim of this book to provide undergraduate and beginning graduate students in mathematics or science and engineering with a modest foundation of knowledge.

Equations in dimensions one and two constitute the majority of the text, and in particular it is 4/5(1). Dynamics and Bifurcations "This book takes the reader step by step through the vast subject of dynamical systems.

Proceeding from 1 to 2 dimensions and onto higher dimensions in separate self-contained sections, the text is mathematically rigorous yet devoid of excess formalism. This volume originates from the Third Nonlinear Control Workshop "- namics, Bifurcations and Control", held in Kloster Irsee, April As the preceding workshops held in Paris () and in Ghent (), it was organized within the framework of Nonlinear Control Network funded by the.

Dynamics and bifurcations by Hale, Jack K. Publication date Topics Bifurcation theory, Differentiable dynamical systems, Differential equations Publisher Borrow this book to access EPUB and PDF files.

IN COLLECTIONS. Books to Borrow. Books for People with Print Disabilities. Trent University Library : Bifurcations of Periodic Equations.

Jack K. Hale, Hüseyin Koçak. one which germinated in applied fields such as celestial mechanics, nonlinear oscillations, and fluid dynamics.

In recent years, due primarily to the proliferation of computers, dynamical systems has once more turned to its roots in applications with perhaps a more mature.

Dynamics and Bifurcations "This book takes the reader step by step through the vast subject of dynamical systems. Proceeding from 1 to 2 dimensions and onto higher dimensions in separate self-contained sections, the text is mathematically rigorous yet devoid of excess : $ This is the third edition of the book.

( views) Introduction to Statics and Dynamics by Rudra Pratap, Andy Ruina - Cornell University, This is an engineering statics and dynamics text intended as both an introduction and as a reference.

The book emphasizes use of vectors, free-body diagrams, momentum and energy balance and computation. Dynamics and Bifurcations "This book takes the reader step by step through the vast subject of dynamical systems.

Proceeding from 1 to 2 dimensions and onto higher dimensions in separate self-contained sections, the text is mathematically rigorous yet devoid of excess formalism/5(8). This volume originates from the Third Nonlinear Control Workshop "- namics, Bifurcations and Control", held in Kloster Irsee, April As the preceding workshops held in Paris () and in Ghe.

Dynamics and Bifurcations of Non-smooth Mechanical Systems presents these developments in a comprehensive way and opens the field to the nonlinear dynamics community. This book addresses researchers and graduate students in engineering and mathematics interested in the modelling, simulation and dynamics of non-smooth systems and nonlinear by: This book discusses the differentiable dynamics, vector fields, fixed points and periodic orbits, and stable and unstable manifolds.

The bifurcations of fixed points of a map and periodic orbits, case of semiflows, and saddle-node and Hopf bifurcation are also elaborated. Dynamics and Bifurcations (Texts in Applied Mathematics, Vol.

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Proceeding from 1 to 2 dimensions and onto higher dimensions in separate self-contained sections, the text is mathematically rigorous yet devoid of excess formalism/5(6). from the very interesting (but di cult) book of Chossat-Lauterbach [2].

One other complementary reference is the book of Golubitsky-Stewart-Schae er [3]. For an elementary review on functional analysis the book of Brezis is recommanded [1]. 1Elementary bifurcation De nition In dynamical systems, a bifurcation occurs when a small smooth changeFile Size: KB.

This monograph combines the knowledge of both the field of nonlinear dynamics and non-smooth mechanics, presenting a framework for a class of non-smooth mechanical systems using techniques from both fields.

The book reviews recent developments, and opens the field to the nonlinear dynamics community. This book addresses researchers and graduate students in engineering and mathematics. Nonlinear Dynamics and Chaos by Strogatz is an introduction to the qualitative study of systems of first degree differential equations.

Topics included through the first six chapters (which is as far as I have currently read) are bifurcations, stability of fixed points, linearization about fixed points, and many others/5. This chapter summarizes the concepts and models associated with chaos and bifurcations.

It reviews the modeling methodology, nonlinear phenomenon, and dynamics of biological populations. Model assessment is important to distinguish between procedures to parameterize (calibrate) a model and those to validate a model.

book Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations: fractal dimensions and infinitely many attractors Palis Jr., Floris Takens Published in in Cited by: This book is an expanded version of a Master Class on the symmetric bifurcation theory of differential equations given by the author at the University of Twente in The notes cover a wide range of recent results in the subject, and focus on the dynamics that can appear in the generic bifurcation theory of symmetric differential equations.

Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family, such as the integral curves of a family of vector fields, and the solutions of a family of differential commonly applied to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation.

Sensitive Chaotic Dynamics at Homoclinic Bifurcations: Fractal Dimensions and Infinitely Many Attractors in Dynamics (Cambridge Studies in Advanced Mathematics) become your current starter. Clyde Okane: Reading a book to become new life style in this year; every people loves to learn a book. When you read a book you can get a great deal of benefit.

Dynamics and Bifurcations has 3 available editions to buy at Half Price Books Marketplace This listing is a new book, a title Show details 4. Trade paperback, Springer, “Chaos and Dynamical Systems is a great introduction to nonlinear dynamics, bifurcations, and chaos.

It is easy to follow and understand, yet also provides a generous amount of mathematical detail, which will satisfy technically oriented minds too. Bifurcations in brain dynamics. Abstract. No abstract available. Save to Binder. Create a New Binder. Name. Cancel; Create; Contributors.

Frank C Hoppensteadt Arizona State University Eugene M Izhikevich Arizona State University Index Terms. J.K. Hale, H. Kocak, and H. Buttanri Dynamics and Bifurcations "This book takes the reader step by step through the vast subject of dynamical systems.

Proceeding from 1 to 2 dimensions and onto higher dimensions in separate self-contained sections, the text is mathematically rigorous yet. change a bit, but overall the dynamics remains essentially the same. Fundamental changes in the dynamics usually only occurs at critical val-ues of µ, termed bifurcation values.

Formally, bifurcations occur at values of µfor which () is not ‘structurally stable’ [1]. Two Parameter Bifurcations. Monkey Saddle Bifurcation. The differential equations controlling the dynamics of the monkey saddle and its bifurcations: dx / dt = f(x, y) = x 2 - y 2 + α, dy / dt = g(x, y) = -2 * x * y + β.

have two parameters, α and β. The system's Jacobian matrix is. The book has two aims. One is to expound the mathematical methods of equivariant bifurcation theory.

Beyond the classical bifurcation tools, such as center manifold and normal form reductions, the presence of symmetry requires the introduction of the algebraic and geometric formalism of Lie group theory and transformation group methods.

Dynamics and Bifurcations, Jack K. Hale, Huseyin Kocak This book is intended for undergraduate and beginning graduate students in mathematics or science and engineering. It has many chapters in one, two (and three) dimensions and was written with lower formalism and is very accessible.

furcation dynamics in terms of an operational con-struction which on the one hand is applicable to a class of autonomous three-dimensional systems and on the other can reflect the particularities of a cho-sen system. In so doing quantitative predictions of bifurcation events can be made within the context of the dynamics speci c to this choice.

Dynamics book reviews. Albers. This is a list of very brief book reviews regarding dynamical systems books as well as background material. These reviews are very informal, are intended for students, are from my personal viewpoint, and thus may not carry much validity.

Mathematical Methods in Nuclear Reactor Dynamics Article (PDF Available) in IEEE Transactions on Plasma Science 3(4) - January with 2, Reads How we measure 'reads'. Introduction to Bifurcations and The Hopf Bifurcation Theorem Roberto Munoz-Alicea~ µ = 0 x Figure 1: Phase portrait for Example We conclude that the equilibrium point x = 0 is an unstable saddle node.

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The book by Leine and Nijmeijer () gives an extensive review of nonsmooth systems and associated bifurcations. The work by Acary and Brogliato () presents a review of numerical methods.

The favorable reaction to the first edition of this book confirmed that the publication of such an application-oriented text on bifurcation theory of dynamical systems was well timed.

The selected topics indeed cover ma-jor practical issues of applying the bifurcation theory to finite-dimensional problems.Book Description. 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.Download Book Dynamics And Bifurcations Texts In Applied Mathematics in PDF format. You can Read Online Dynamics And Bifurcations Texts In Applied Mathematics here in PDF, EPUB, Mobi or Docx formats.

Dynamics and Bifurcations. Author: Jack K. Hale,Hüseyin Kocak. Publisher: Springer Science & .

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