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Dynamic Bifurcations

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Dynamic Bifurcations

Dynamic Bifurcations Book
Author : Eric Benoit
Publisher : Springer
Release : 2006-11-14
ISBN : 3540464719
File Size : 42,6 Mb
Language : En, Es, Fr and De

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Dynamic Bifurcations Book PDF/Epub Download

Dynamical Bifurcation Theory is concerned with the phenomena that occur in one parameter families of dynamical systems (usually ordinary differential equations), when the parameter is a slowly varying function of time. During the last decade these phenomena were observed and studied by many mathematicians, both pure and applied, from eastern and western countries, using classical and nonstandard analysis. It is the purpose of this book to give an account of these developments. The first paper, by C. Lobry, is an introduction: the reader will find here an explanation of the problems and some easy examples; this paper also explains the role of each of the other paper within the volume and their relationship to one another. CONTENTS: C. Lobry: Dynamic Bifurcations.- T. Erneux, E.L. Reiss, L.J. Holden, M. Georgiou: Slow Passage through Bifurcation and Limit Points. Asymptotic Theory and Applications.- M. Canalis-Durand: Formal Expansion of van der Pol Equation Canard Solutions are Gevrey.- V. Gautheron, E. Isambert: Finitely Differentiable Ducks and Finite Expansions.- G. Wallet: Overstability in Arbitrary Dimension.- F.Diener, M. Diener: Maximal Delay.- A. Fruchard: Existence of Bifurcation Delay: the Discrete Case.- C. Baesens: Noise Effect on Dynamic Bifurcations:the Case of a Period-doubling Cascade.- E. Benoit: Linear Dynamic Bifurcation with Noise.- A. Delcroix: A Tool for the Local Study of Slow-fast Vector Fields: the Zoom.- S.N. Samborski: Rivers from the Point ofView of the Qualitative Theory.- F. Blais: Asymptotic Expansions of Rivers.-I.P. van den Berg: Macroscopic Rivers.

Dynamics and Bifurcations

Dynamics and Bifurcations Book
Author : Jack K. Hale,Hüseyin Kocak
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 1461244269
File Size : 26,8 Mb
Language : En, Es, Fr and De

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Dynamics and Bifurcations Book PDF/Epub Download

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.

Topics in Dynamic Bifurcation Theory

Topics in Dynamic Bifurcation Theory Book
Author : Jack K. Hale
Publisher : American Mathematical Soc.
Release : 1981-12-31
ISBN : 0821816985
File Size : 45,9 Mb
Language : En, Es, Fr and De

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Topics in Dynamic Bifurcation Theory Book PDF/Epub Download

Presents the general theory of first order bifurcation that occur for vector fields in finite dimensional space. This book includes formulation of structural stability and bifurcation in infinite dimensions.

Dynamics Bifurcations and Control

Dynamics  Bifurcations and Control Book
Author : Fritz Colonius,Lars Grüne
Publisher : Springer
Release : 2003-07-01
ISBN : 3540456066
File Size : 37,8 Mb
Language : En, Es, Fr and De

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Dynamics Bifurcations and Control Book PDF/Epub Download

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.

Nonlinear Oscillations Dynamical Systems and Bifurcations of Vector Fields

Nonlinear Oscillations  Dynamical Systems  and Bifurcations of Vector Fields Book
Author : John Guckenheimer,Philip Holmes
Publisher : Unknown
Release : 2014-09-01
ISBN : 9781461211419
File Size : 24,8 Mb
Language : En, Es, Fr and De

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Nonlinear Oscillations Dynamical Systems and Bifurcations of Vector Fields Book PDF/Epub Download

Download Nonlinear Oscillations Dynamical Systems and Bifurcations of Vector Fields book written by John Guckenheimer,Philip Holmes and published by with total hardcover pages 484 . Available in PDF, EPUB, and Kindle, read book directly with any devices anywhere and anytime.

Dynamic Modelling Bifurcation and Chaotic Behaviour of Gas Solid Catalytic Reactors

Dynamic Modelling  Bifurcation and Chaotic Behaviour of Gas Solid Catalytic Reactors Book
Author : S. S. E. H. Elnashaie
Publisher : CRC Press
Release : 1996-03-18
ISBN : 9782884490788
File Size : 23,9 Mb
Language : En, Es, Fr and De

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Dynamic Modelling Bifurcation and Chaotic Behaviour of Gas Solid Catalytic Reactors Book PDF/Epub Download

The discovery of chaos has considerably widened the scope of our knowledge regarding the dynamics of physical systems. Gas-solid catalytic reactors are important units in the petrochemical and petroleum refining industries and in the field of environmental protection. The knowledge required to understand and analyse the bifurcation, dynamics and chaotic behaviour of these reactors is widespread among many disciplines including chemical reaction, engineering, chemistry, physics and pure and applied mathematics. This book is the first to consolidate the progress in understanding the complex dynamics of catalytic reactors. It covers the most important aspects of the problem, which includes the formulation of the dynamic models for these systems, the basic dynamic, bifurcation and chaotic characteristics of the different types and configurations of these units, the industrial relevance of these complex dynamic phenomena, as well as the mathematical tools necessary for the detailed analysis of these complex dynamics. This book is easy to read, and will therefore appeal to a wide spectrum of chemical engineering students and chemical engineers in academia and in industry, also students and researchers from other disciplines who are interested in the rich and fascinating complex dynamic characteristics of gas-solid catalytic reactors, will find it both interesting and useful.

Dynamics and Bifurcations of Non Smooth Mechanical Systems

Dynamics and Bifurcations of Non Smooth Mechanical Systems Book
Author : Remco I. Leine,Henk Nijmeijer
Publisher : Springer Science & Business Media
Release : 2013-03-19
ISBN : 3540443983
File Size : 28,5 Mb
Language : En, Es, Fr and De

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Dynamics and Bifurcations of Non Smooth Mechanical Systems Book PDF/Epub Download

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

Elements of Differentiable Dynamics and Bifurcation Theory Book
Author : David Ruelle
Publisher : Elsevier
Release : 2014-05-10
ISBN : 1483272184
File Size : 21,9 Mb
Language : En, Es, Fr and De

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Elements of Differentiable Dynamics and Bifurcation Theory Book PDF/Epub Download

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.

Numerical Methods for Bifurcations of Dynamical Equilibria

Numerical Methods for Bifurcations of Dynamical Equilibria Book
Author : Willy J. F. Govaerts
Publisher : SIAM
Release : 2000-01-01
ISBN : 9780898719543
File Size : 35,6 Mb
Language : En, Es, Fr and De

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Numerical Methods for Bifurcations of Dynamical Equilibria Book PDF/Epub Download

Dynamical systems arise in all fields of applied mathematics. The author focuses on the description of numerical methods for the detection, computation, and continuation of equilibria and bifurcation points of equilibria of dynamical systems. This subfield has the particular attraction of having links with the geometric theory of differential equations, numerical analysis, and linear algebra.

Numerical Methods for Bifurcation Problems and Large Scale Dynamical Systems

Numerical Methods for Bifurcation Problems and Large Scale Dynamical Systems Book
Author : Eusebius Doedel,Laurette S. Tuckerman
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 1461212081
File Size : 49,8 Mb
Language : En, Es, Fr and De

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Numerical Methods for Bifurcation Problems and Large Scale Dynamical Systems Book PDF/Epub Download

The Institute for Mathematics and its Applications (IMA) devoted its 1997-1998 program to Emerging Applications of Dynamical Systems. Dynamical systems theory and related numerical algorithms provide powerful tools for studying the solution behavior of differential equations and mappings. In the past 25 years computational methods have been developed for calculating fixed points, limit cycles, and bifurcation points. A remaining challenge is to develop robust methods for calculating more complicated objects, such as higher- codimension bifurcations of fixed points, periodic orbits, and connecting orbits, as well as the calcuation of invariant manifolds. Another challenge is to extend the applicability of algorithms to the very large systems that result from discretizing partial differential equations. Even the calculation of steady states and their linear stability can be prohibitively expensive for large systems (e.g. 10_3- -10_6 equations) if attempted by simple direct methods. Several of the papers in this volume treat computational methods for low and high dimensional systems and, in some cases, their incorporation into software packages. A few papers treat fundamental theoretical problems, including smooth factorization of matrices, self -organized criticality, and unfolding of singular heteroclinic cycles. Other papers treat applications of dynamical systems computations in various scientific fields, such as biology, chemical engineering, fluid mechanics, and mechanical engineering.

Dynamics and Bifurcations of Non Smooth Mechanical Systems

Dynamics and Bifurcations of Non Smooth Mechanical Systems Book
Author : Remco Leine,Henk Nijmeijer
Publisher : Springer Science & Business Media
Release : 2006-06-13
ISBN : 9783540219873
File Size : 35,7 Mb
Language : En, Es, Fr and De

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Dynamics and Bifurcations of Non Smooth Mechanical Systems Book PDF/Epub Download

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.

Attractivity and Bifurcation for Nonautonomous Dynamical Systems

Attractivity and Bifurcation for Nonautonomous Dynamical Systems Book
Author : Martin Rasmussen
Publisher : Springer Science & Business Media
Release : 2007-06-08
ISBN : 3540712240
File Size : 53,8 Mb
Language : En, Es, Fr and De

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Attractivity and Bifurcation for Nonautonomous Dynamical Systems Book PDF/Epub Download

Although, bifurcation theory of equations with autonomous and periodic time dependence is a major object of research in the study of dynamical systems since decades, the notion of a nonautonomous bifurcation is not yet established. In this book, two different approaches are developed which are based on special definitions of local attractivity and repulsivity. It is shown that these notions lead to nonautonomous Morse decompositions.

Methods in Equivariant Bifurcations and Dynamical Systems

Methods in Equivariant Bifurcations and Dynamical Systems Book
Author : Pascal Chossat,Reiner Lauterbach
Publisher : World Scientific Publishing Company
Release : 2000-02-28
ISBN : 9813105445
File Size : 30,7 Mb
Language : En, Es, Fr and De

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Methods in Equivariant Bifurcations and Dynamical Systems Book PDF/Epub Download

This invaluable book presents a comprehensive introduction to bifurcation theory in the presence of symmetry, an applied mathematical topic which has developed considerably over the past twenty years and has been very successful in analysing and predicting pattern formation and other critical phenomena in most areas of science where nonlinear models are involved, like fluid flow instabilities, chemical waves, elasticity and population dynamics. 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. For the first time, all these methods in equivariant bifurcations are presented in a coherent and self-consistent way in a book. The other aim is to present the most recent ideas and results in this theory, in relation to applications. This includes bifurcations of relative equilibria and relative periodic orbits for compact and noncompact group actions, heteroclinic cycles and forced symmetry-breaking perturbations. Although not all recent contributions could be included and a choice had to be made, a rather complete description of these new developments is provided. At the end of every chapter, exercises are offered to the reader.

Bifurcation Theory and Methods of Dynamical Systems

Bifurcation Theory and Methods of Dynamical Systems Book
Author : Luo Dingjun,Wang Xian,Zhu Deming,Han Maoan
Publisher : World Scientific
Release : 1997-11-29
ISBN : 9814501093
File Size : 53,5 Mb
Language : En, Es, Fr and De

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Bifurcation Theory and Methods of Dynamical Systems Book PDF/Epub Download

Dynamical bifurcation theory is concerned with the changes that occur in the global structure of dynamical systems as parameters are varied. This book makes recent research in bifurcation theory of dynamical systems accessible to researchers interested in this subject. In particular, the relevant results obtained by Chinese mathematicians are introduced as well as some of the works of the authors which may not be widely known. The focus is on the analytic approach to the theory and methods of bifurcations. The book prepares graduate students for further study in this area, and it serves as a ready reference for researchers in nonlinear sciences and applied mathematics. Contents:Basic Concepts and FactsBifurcation of 2-Dimensional SystemsBifurcation in Polynomial Liénard SystemsPeriodic Perturbed Systems and Integral ManifoldsBifurcations of Higher Dimensional SystemsMelnikov Vector, Homoclinic and Heteroclinic Orbits Readership: Nonlinear scientists, mathematicians and physicists. keywords:Dynamical System;Invariant Torus;Periodic Solution;Limit Cycle;Melnikov Function;Chootic Dynamics;Polynomial System;Homoclinic Loop;Poly-Cycle;Subharmonic Solution;Silnikov Phynomenon and Chaos;Lienard System;Perturbation Theory

Elements of Applied Bifurcation Theory

Elements of Applied Bifurcation Theory Book
Author : Yuri Kuznetsov
Publisher : Springer Science & Business Media
Release : 2013-03-09
ISBN : 1475739788
File Size : 42,6 Mb
Language : En, Es, Fr and De

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Elements of Applied Bifurcation Theory Book PDF/Epub Download

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.

Local Bifurcations Center Manifolds and Normal Forms in Infinite Dimensional Dynamical Systems

Local Bifurcations  Center Manifolds  and Normal Forms in Infinite Dimensional Dynamical Systems Book
Author : Mariana Haragus,Gérard Iooss
Publisher : Springer Science & Business Media
Release : 2010-11-23
ISBN : 0857291122
File Size : 29,6 Mb
Language : En, Es, Fr and De

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Local Bifurcations Center Manifolds and Normal Forms in Infinite Dimensional Dynamical Systems Book PDF/Epub Download

An extension of different lectures given by the authors, Local Bifurcations, Center Manifolds, and Normal Forms in Infinite Dimensional Dynamical Systems provides the reader with a comprehensive overview of these topics. Starting with the simplest bifurcation problems arising for ordinary differential equations in one- and two-dimensions, this book describes several tools from the theory of infinite dimensional dynamical systems, allowing the reader to treat more complicated bifurcation problems, such as bifurcations arising in partial differential equations. Attention is restricted to the study of local bifurcations with a focus upon the center manifold reduction and the normal form theory; two methods that have been widely used during the last decades. Through use of step-by-step examples and exercises, a number of possible applications are illustrated, and allow the less familiar reader to use this reduction method by checking some clear assumptions. Written by recognised experts in the field of center manifold and normal form theory this book provides a much-needed graduate level text on bifurcation theory, center manifolds and normal form theory. It will appeal to graduate students and researchers working in dynamical system theory.

Nonlinear Oscillations Dynamical Systems and Bifurcations of Vector Fields

Nonlinear Oscillations  Dynamical Systems  and Bifurcations of Vector Fields Book
Author : John Guckenheimer,Philip Holmes
Publisher : Springer Science & Business Media
Release : 2013-11-21
ISBN : 1461211409
File Size : 50,6 Mb
Language : En, Es, Fr and De

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Nonlinear Oscillations Dynamical Systems and Bifurcations of Vector Fields Book PDF/Epub Download

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.

Fundamentals of Dynamical Systems and Bifurcation Theory

Fundamentals of Dynamical Systems and Bifurcation Theory Book
Author : Milan Medved̕,̕ Milan Medved (RNDr.)
Publisher : CRC Press
Release : 1992-05-21
ISBN : 9780750301503
File Size : 32,9 Mb
Language : En, Es, Fr and De

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Fundamentals of Dynamical Systems and Bifurcation Theory Book PDF/Epub Download

This graduate level text explains the fundamentals of the theory of dynamical systems. After reading it you will have a good enough understanding of the area to study the extensive literature on dynamical systems. The book is self contained, as all the essential definitions and proofs are supplied, as are useful references: all the reader needs is a knowledge of basic mathematical analysis, algebra and topology. However, the first chapter contains an explanation of some of the methods of differential topology an understanding of which is essential to the theory of dynamical systems. A clear introduction to the field, which is equally useful for postgraduates in the natural sciences, engineering and economics.

Discrete Dynamical Systems Bifurcations and Chaos in Economics

Discrete Dynamical Systems  Bifurcations and Chaos in Economics Book
Author : Wei-Bin Zhang
Publisher : Elsevier
Release : 2006-01-05
ISBN : 9780080462462
File Size : 29,9 Mb
Language : En, Es, Fr and De

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Discrete Dynamical Systems Bifurcations and Chaos in Economics Book PDF/Epub Download

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

Hopf Bifurcation Analysis

Hopf Bifurcation Analysis Book
Author : Jorge L Moiola,Guanrong Chen
Publisher : World Scientific
Release : 1996-04-09
ISBN : 9814499102
File Size : 53,9 Mb
Language : En, Es, Fr and De

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Hopf Bifurcation Analysis Book PDF/Epub Download

This book is devoted to the frequency domain approach, for both regular and degenerate Hopf bifurcation analyses. Besides showing that the time and frequency domain approaches are in fact equivalent, the fact that many significant results and computational formulas obtained in the studies of regular and degenerate Hopf bifurcations from the time domain approach can be translated and reformulated into the corresponding frequency domain setting, and be reconfirmed and rediscovered by using the frequency domain methods, is also explained. The description of how the frequency domain approach can be used to obtain several types of standard bifurcation conditions for general nonlinear dynamical systems is given as well as is demonstrated a very rich pictorial gallery of local bifurcation diagrams for nonlinear systems under simultaneous variations of several system parameters. In conjunction with this graphical analysis of local bifurcation diagrams, the defining and nondegeneracy conditions for several degenerate Hopf bifurcations is presented. With a great deal of algebraic computation, some higher-order harmonic balance approximation formulas are derived, for analyzing the dynamical behavior in small neighborhoods of certain types of degenerate Hopf bifurcations that involve multiple limit cycles and multiple limit points of periodic solutions. In addition, applications in chemical, mechanical and electrical engineering as well as in biology are discussed. This book is designed and written in a style of research monographs rather than classroom textbooks, so that the most recent contributions to the field can be included with references. Contents: IntroductionThe Hopf Bifurcation TheoremContinuation of Bifurcation Curves on the Parameter PlaneDegenerate Bifurcations in the Space of System ParametersHigh-Order Hopf Bifurcation FormulasHopf Bifurcation in Nonlinear Systems with Time DelaysBirth of Multiple Limit CyclesAppendixReferencesArthur IndexSubject Index Readership: Nonlinear scientists, applied mathematicians, and systems engineers. keywords:Bifurcation;Harmonic Balance Approximation;Graphical Hopf Bifurcation;Degenerate Hopf Bifurcation;High-Order Hopf Bifurcation;Multiple Limit Cycles;Hopf;Frequency;Harmonic Balance;Feedback;Oscillations;Nonlinear;Delay;Limit Cycles;Degenerate Bifurcations

Dynamical Systems V

Dynamical Systems V Book
Author : V.I. Arnold,V.S. Afrajmovich,Yu.S. Il'yashenko,L.P. Shil'nikov
Publisher : Springer Science & Business Media
Release : 2013-12-01
ISBN : 3642578845
File Size : 39,5 Mb
Language : En, Es, Fr and De

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Dynamical Systems V Book PDF/Epub Download

Bifurcation theory and catastrophe theory are two well-known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems. Catastrophe theory became quite famous during the 1970's, mostly because of the sensation caused by the usually less than rigorous applications of its principal ideas to "hot topics", such as the characterization of personalities and the difference between a "genius" and a "maniac". Catastrophe theory is accurately described as singularity theory and its (genuine) applications. The authors of this book, previously published as Volume 5 of the Encyclopaedia, have given a masterly exposition of these two theories, with penetrating insight.