Bifurcation Without Parameters
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Bifurcation Without Parameters
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Author : Stefan Liebscher
language : en
Publisher: Springer
Release Date : 2014-11-08
Bifurcation Without Parameters written by Stefan Liebscher and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-08 with Mathematics categories.
Targeted at mathematicians having at least a basic familiarity with classical bifurcation theory, this monograph provides a systematic classification and analysis of bifurcations without parameters in dynamical systems. Although the methods and concepts are briefly introduced, a prior knowledge of center-manifold reductions and normal-form calculations will help the reader to appreciate the presentation. Bifurcations without parameters occur along manifolds of equilibria, at points where normal hyperbolicity of the manifold is violated. The general theory, illustrated by many applications, aims at a geometric understanding of the local dynamics near the bifurcation points.
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.
Bifurcation Theory
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Author : Ale Jan Homburg
language : en
Publisher: American Mathematical Society
Release Date : 2024-12-02
Bifurcation Theory written by Ale Jan Homburg and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-02 with Mathematics categories.
This textbook provides a thorough overview of bifurcation theory. Assuming some familiarity with differential equations and dynamical systems, it is suitable for use on advanced undergraduate and graduate level and can, in particular, be used for a graduate course on bifurcation theory. The book combines a solid theoretical basis with a detailed description of classical bifurcations. It is organized in chapters on local, nonlocal, and global bifurcations; a number of appendices develop the toolbox for the study of bifurcations. The discussed local bifurcations include saddle-node and Hopf bifurcations, as well as the more advanced Bogdanov-Takens and Neimark-Sacker bifurcations. The book also covers nonlocal bifurcations, discussing various homoclinic bifurcations, and it surveys global bifurcations and phenomena, such as intermittency and period-doubling cascades. The book develops a broad range of complementary techniques, both geometric and analytic, for studying bifurcations. Techniques include normal form methods, center manifold reductions, the Lyapunov-Schmidt construction, cross-coordinate constructions, Melnikov's method, and Lin's method. Full proofs of the results are provided, also for the material in the appendices. This includes proofs of the stable manifold theorem, of the center manifold theorem, and of Lin's method for studying homoclinic bifurcations.
Numerical Methods For Bifurcations Of Dynamical Equilibria
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Author : Willy J. F. Govaerts
language : en
Publisher: SIAM
Release Date : 2000-01-01
Numerical Methods For Bifurcations Of Dynamical Equilibria written by Willy J. F. Govaerts and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-01 with Mathematics categories.
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.
Elements Of Applied Bifurcation Theory
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Author : Yuri Kuznetsov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
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 2013-03-09 with Mathematics categories.
The years that have passed since the publication of the first edition of this book proved that the basic principles used to select and present the material made sense. The idea was to write a simple text that could serve as a seri ous introduction to the subject. Of course, the meaning of "simplicity" varies from person to person and from country to country. The word "introduction" contains even more ambiguity. To start reading this book, only a moder ate knowledge of linear algebra and calculus is required. Other preliminaries, qualified as "elementary" in modern mathematics, are explicitly formulated in the book. These include the Fredholm Alternative for linear systems and the multidimensional Implicit Function Theorem. Using these very limited tools, a framewo:k of notions, results, and methods is gradually built that allows one to read (and possibly write) scientific papers on bifurcations of nonlinear dynamical systems. Among other things, progress in the sciences means that mathematical results and methods that once were new become standard and routinely used by the research and development community. Hopefully, this edition of the book will contribute to this process. The book's structure has been kept intact. Most of the changes introduced reflect recent theoretical and software developments in which the author was involved. Important changes in the third edition can be summarized as follows. A new section devoted to the fold-flip bifurcation for maps has appeared in Chapter 9.
Elements Of Applied Bifurcation Theory
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Author : Yuri A. Kuznetsov
language : en
Publisher: Springer Nature
Release Date : 2023-04-18
Elements Of Applied Bifurcation Theory written by Yuri A. Kuznetsov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-18 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.
Numerical Continuation And Bifurcation In Nonlinear Pdes
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Author : Hannes Uecker
language : en
Publisher: SIAM
Release Date : 2021-08-19
Numerical Continuation And Bifurcation In Nonlinear Pdes written by Hannes Uecker and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-19 with Mathematics categories.
This book provides a hands-on approach to numerical continuation and bifurcation for nonlinear PDEs in 1D, 2D, and 3D. Partial differential equations (PDEs) are the main tool to describe spatially and temporally extended systems in nature. PDEs usually come with parameters, and the study of the parameter dependence of their solutions is an important task. Letting one parameter vary typically yields a branch of solutions, and at special parameter values, new branches may bifurcate. After a concise review of some analytical background and numerical methods, the author explains the free MATLAB package pde2path by using a large variety of examples with demo codes that can be easily adapted to the reader's given problem. Numerical Continuation and Bifurcation in Nonlinear PDEs will appeal to applied mathematicians and scientists from physics, chemistry, biology, and economics interested in the numerical solution of nonlinear PDEs, particularly the parameter dependence of solutions. It can be used as a supplemental text in courses on nonlinear PDEs and modeling and bifurcation.
Electronic Modelling Of Deterministic And Stochastic Oscillators
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Author : Vladimir Semenov
language : en
Publisher: Springer Nature
Release Date : 2025-01-28
Electronic Modelling Of Deterministic And Stochastic Oscillators written by Vladimir Semenov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-28 with Science categories.
This book presents advanced methods for the electronic modeling of dynamical systems governed by ordinary differential equations. It offers a comprehensive toolkit and practical solutions for specialists in nonlinear dynamics who seek experimental validation of their mathematical models. The aim is to empower readers without an extensive background in electronics or circuit theory to translate their theoretical concepts into real-world devices, facilitating the rapid experimental confirmation of numerical and theoretical findings. For experts in electronic engineering, the book showcases how a wide range of non-electronic systems and their unique characteristics can be effectively modeled using electronic circuits. Bridging the gap between theory and practice, the book serves as a valuable resource on electronics for theorists and mathematicians, and on nonlinear dynamics for experimentalists and engineers. Its audience includes a broad spectrum of readers, from students and engineers to scientists and researchers across various fields.
Bifurcation Theory Of Functional Differential Equations
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Author : Shangjiang Guo
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-30
Bifurcation Theory Of Functional Differential Equations written by Shangjiang Guo 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 2013-07-30 with Mathematics categories.
This book provides a crash course on various methods from the bifurcation theory of Functional Differential Equations (FDEs). FDEs arise very naturally in economics, life sciences and engineering and the study of FDEs has been a major source of inspiration for advancement in nonlinear analysis and infinite dimensional dynamical systems. The book summarizes some practical and general approaches and frameworks for the investigation of bifurcation phenomena of FDEs depending on parameters with chap. This well illustrated book aims to be self contained so the readers will find in this book all relevant materials in bifurcation, dynamical systems with symmetry, functional differential equations, normal forms and center manifold reduction. This material was used in graduate courses on functional differential equations at Hunan University (China) and York University (Canada).
Elements Of Applied Bifurcation Theory
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Author : I︠U︡riĭ Aleksandrovich Kuznet︠s︡ov
language : en
Publisher: Springer
Release Date : 1995-06-13
Elements Of Applied Bifurcation Theory written by I︠U︡riĭ Aleksandrovich Kuznet︠s︡ov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-06-13 with Mathematics categories.
A solid basis for anyone studying the dynamical systems theory, providing the necessary understanding of the approaches, methods, results and terminology used in the modern applied-mathematics literature. Covering the basic topics in the field, the text can be used in a course on nonlinear dynamical systems or system theory. Special attention is given to efficient numerical implementations of the developed techniques, illustrated by several examples from recent research papers. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used, making this book suitable for advanced undergraduate or graduate students in applied mathematics, as well as for researchers in other disciplines who use dynamical systems as model tools in their studies.