Dynamics And Bifurcations

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Dynamics And Bifurcations

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Author : Jack K. Hale
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Dynamics And Bifurcations written by Jack K. Hale and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

The subject of differential and difference equations is an old and much-honored chapter in science, 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 look. Many of the available books and expository narratives either require extensive mathematical preparation, or are not designed to be used as textbooks. The authors have filled this void with the present book.

Dynamics And Bifurcations Of Non Smooth Mechanical Systems

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Author : Remco Leine
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-13

Dynamics And Bifurcations Of Non Smooth Mechanical Systems written by Remco Leine and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-13 with Mathematics categories.

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 interested in the modelling, simulation and dynamics of non-smooth systems and nonlinear dynamics.

Elements Of Differentiable Dynamics And Bifurcation Theory

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Author : David Ruelle
language : en
Publisher: Elsevier
Release Date : 2014-05-10

Elements Of Differentiable Dynamics And Bifurcation Theory written by David Ruelle and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.

Elements of Differentiable Dynamics and Bifurcation Theory provides an introduction to differentiable dynamics, with emphasis on bifurcation theory and hyperbolicity that is essential for the understanding of complicated time evolutions occurring in nature. 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. This text likewise covers the persistence of normally hyperbolic manifolds, hyperbolic sets, homoclinic and heteroclinic intersections, and global bifurcations. This publication is suitable for mathematicians and mathematically inclined students of the natural sciences.

Dynamics And Bifurcations

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Author : Jack K. Hale
language : en
Publisher: Springer
Release Date : 1991-01

Dynamics And Bifurcations written by Jack K. Hale and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-01 with Bifurcation theory categories.

Elements Of Applied Bifurcation Theory

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Author : Yuri Kuznetsov
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-06-29

Elements Of Applied Bifurcation Theory written by Yuri Kuznetsov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-29 with Mathematics categories.

Providing readers with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems, the focus here is on efficient numerical implementations of the developed techniques. The book is designed for advanced undergraduates or graduates in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the first while updating the context to incorporate recent theoretical developments, in particular new and improved numerical methods for bifurcation analysis.

Dynamical Systems Bifurcation Analysis And Applications

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Author : Mohd Hafiz Mohd
language : en
Publisher: Springer Nature
Release Date : 2019-10-11

Dynamical Systems Bifurcation Analysis And Applications written by Mohd Hafiz Mohd and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-11 with Mathematics categories.

This book is the result of ​Southeast Asian Mathematical Society (SEAMS) School 2018 on Dynamical Systems and Bifurcation Analysis (DySBA). It addresses the latest developments in the field of dynamical systems, and highlights the importance of numerical continuation studies in tracking both stable and unstable steady states and bifurcation points to gain better understanding of the dynamics of the systems. The SEAMS School 2018 on DySBA was held in Penang from 6th to 13th August at the School of Mathematical Sciences, Universiti Sains Malaysia.The SEAMS Schools are part of series of intensive study programs that aim to provide opportunities for an advanced learning experience in mathematics via planned lectures, contributed talks, and hands-on workshop. This book will appeal to those postgraduates, lecturers and researchers working in the field of dynamical systems and their applications. Senior undergraduates in Mathematics will also find it useful.

Dynamics And Bifurcations

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Author : Jack K. Hale
language : en
Publisher: Springer
Release Date : 1996-12-01

Dynamics And Bifurcations written by Jack K. Hale and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-12-01 with Mathematics categories.

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 demonstrated that the basic notion of stability and bifurcations of vector fields are easily explained for scalar autonomous equations. Further, the authors investigate the dynamics of planar autonomous equations where new dynamical behavior, such as periodic and homoclinic orbits appears.

Hyperbolicity And Sensitive Chaotic Dynamics At Homoclinic Bifurcations

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Author : Jacob Palis Júnior
language : en
Publisher: Cambridge University Press
Release Date : 1995-01-05

Hyperbolicity And Sensitive Chaotic Dynamics At Homoclinic Bifurcations written by Jacob Palis Júnior and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-01-05 with Mathematics categories.

A self-contained introduction to the classical theory and its generalizations, aimed at mathematicians and scientists working in dynamical systems.

Nonlinear Oscillations Dynamical Systems And Bifurcations Of Vector Fields

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Author : John Guckenheimer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-21

Nonlinear Oscillations Dynamical Systems And Bifurcations Of Vector Fields written by John Guckenheimer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-21 with Mathematics categories.

From the reviews: "This book is concerned with the application of methods from dynamical systems and bifurcation theories to the study of nonlinear oscillations. Chapter 1 provides a review of basic results in the theory of dynamical systems, covering both ordinary differential equations and discrete mappings. Chapter 2 presents 4 examples from nonlinear oscillations. Chapter 3 contains a discussion of the methods of local bifurcation theory for flows and maps, including center manifolds and normal forms. Chapter 4 develops analytical methods of averaging and perturbation theory. Close analysis of geometrically defined two-dimensional maps with complicated invariant sets is discussed in chapter 5. Chapter 6 covers global homoclinic and heteroclinic bifurcations. The final chapter shows how the global bifurcations reappear in degenerate local bifurcations and ends with several more models of physical problems which display these behaviors." #Book Review - Engineering Societies Library, New York#1 "An attempt to make research tools concerning `strange attractors' developed in the last 20 years available to applied scientists and to make clear to research mathematicians the needs in applied works. Emphasis on geometric and topological solutions of differential equations. Applications mainly drawn from nonlinear oscillations." #American Mathematical Monthly#2

Dynamics Bifurcations And Control

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Author : Fritz Colonius
language : en
Publisher: Springer
Release Date : 2003-07-01

Dynamics Bifurcations And Control written by Fritz Colonius and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-01 with Technology & Engineering categories.

This volume originates from the Third Nonlinear Control Workshop "- namics, Bifurcations and Control", held in Kloster Irsee, April 1-3 2001. As the preceding workshops held in Paris (2000) and in Ghent (1999), it was organized within the framework of Nonlinear Control Network funded by the European Union (http://www.supelec.fr/lss/NCN). The papers in this volume center around those control problems where phenomena and methods from dynamical systems theory play a dominant role. Despite the large variety of techniques and methods present in the c- tributions, a rough subdivision can be given into three areas: Bifurcation problems, stabilization and robustness, and global dynamics of control s- tems. A large part of the fascination in nonlinear control stems from the fact that is deeply rooted in engineering and mathematics alike. The contributions to this volume reflect this double nature of nonlinear control. We would like to take this opportunity to thank all the contributors and the referees for their careful work. Furthermore, it is our pleasure to thank Franchise Lamnabhi-Lagarrigue, the coordinator of our network, for her s- port in organizing the workshop and the proceedings and for the tremendous efforts she puts into this network bringing the cooperation between the d- ferent groups to a new level. In particular, the exchange and the active p- ticipation of young scientists, also reflected in the Pedagogical Schools within the Network, is an asset for the field of nonlinear control.