Elements Of Applied Bifurcation Theory
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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.
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.
Elements Of Applied Bifurcation Theory
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Author : Yuri A. Kuznetsov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Elements Of Applied Bifurcation Theory written by Yuri A. 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.
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.
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.
Elements Of Applied Bifurcation Theory
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Author : Yuri Aleksandrovich Kuznetsov
language : en
Publisher:
Release Date : 1995
Elements Of Applied Bifurcation Theory written by Yuri Aleksandrovich Kuznetsov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with categories.
Elements Of Applied Bifurcation Theory
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Author : Yuri Kuznetsov
language : en
Publisher: Springer
Release Date : 1998-09-18
Elements Of Applied Bifurcation Theory written by Yuri Kuznetsov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-09-18 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.
Methods Of Bifurcation Theory
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Author : S.-N. Chow
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Methods Of Bifurcation Theory written by S.-N. Chow 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.
An alternative title for this book would perhaps be Nonlinear Analysis, Bifurcation Theory and Differential Equations. Our primary objective is to discuss those aspects of bifurcation theory which are particularly meaningful to differential equations. To accomplish this objective and to make the book accessible to a wider we have presented in detail much of the relevant background audience, material from nonlinear functional analysis and the qualitative theory of differential equations. Since there is no good reference for some of the mate rial, its inclusion seemed necessary. Two distinct aspects of bifurcation theory are discussed-static and dynamic. Static bifurcation theory is concerned with the changes that occur in the structure of the set of zeros of a function as parameters in the function are varied. If the function is a gradient, then variational techniques play an important role and can be employed effectively even for global problems. If the function is not a gradient or if more detailed information is desired, the general theory is usually local. At the same time, the theory is constructive and valid when several independent parameters appear in the function. In differential equations, the equilibrium solutions are the zeros of the vector field. Therefore, methods in static bifurcation theory are directly applicable.
Bifurcation Theory
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Author : Hansjörg Kielhöfer
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-13
Bifurcation Theory written by Hansjörg Kielhöfer 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 2011-11-13 with Mathematics categories.
In the past three decades, bifurcation theory has matured into a well-established and vibrant branch of mathematics. This book gives a unified presentation in an abstract setting of the main theorems in bifurcation theory, as well as more recent and lesser known results. It covers both the local and global theory of one-parameter bifurcations for operators acting in infinite-dimensional Banach spaces, and shows how to apply the theory to problems involving partial differential equations. In addition to existence, qualitative properties such as stability and nodal structure of bifurcating solutions are treated in depth. This volume will serve as an important reference for mathematicians, physicists, and theoretically-inclined engineers working in bifurcation theory and its applications to partial differential equations. The second edition is substantially and formally revised and new material is added. Among this is bifurcation with a two-dimensional kernel with applications, the buckling of the Euler rod, the appearance of Taylor vortices, the singular limit process of the Cahn-Hilliard model, and an application of this method to more complicated nonconvex variational problems.
Numerical Bifurcation Analysis Of Maps
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Author : I︠U︡riĭ Aleksandrovich Kuznet︠s︡ov
language : en
Publisher: Cambridge University Press
Release Date : 2019-03-28
Numerical Bifurcation Analysis Of Maps written by I︠U︡riĭ Aleksandrovich Kuznet︠s︡ov 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 2019-03-28 with Mathematics categories.
Combines a systematic analysis of bifurcations of iterated maps with concrete MATLAB® implementations and applications.
Singularities And Groups In Bifurcation Theory
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Author : Martin Golubitsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
Singularities And Groups In Bifurcation Theory written by Martin Golubitsky 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 2013-11-27 with Mathematics categories.
This book has been written in a frankly partisian spirit-we believe that singularity theory offers an extremely useful approach to bifurcation prob lems and we hope to convert the reader to this view. In this preface we will discuss what we feel are the strengths of the singularity theory approach. This discussion then Ieads naturally into a discussion of the contents of the book and the prerequisites for reading it. Let us emphasize that our principal contribution in this area has been to apply pre-existing techniques from singularity theory, especially unfolding theory and classification theory, to bifurcation problems. Many ofthe ideas in this part of singularity theory were originally proposed by Rene Thom; the subject was then developed rigorously by John Matherand extended by V. I. Arnold. In applying this material to bifurcation problems, we were greatly encouraged by how weil the mathematical ideas of singularity theory meshed with the questions addressed by bifurcation theory. Concerning our title, Singularities and Groups in Bifurcation Theory, it should be mentioned that the present text is the first volume in a two-volume sequence. In this volume our emphasis is on singularity theory, with group theory playing a subordinate role. In Volume II the emphasis will be more balanced. Having made these remarks, Iet us set the context for the discussion of the strengths of the singularity theory approach to bifurcation. As we use the term, bifurcation theory is the study of equations with multiple solutions.
Dynamics Of The Chemostat
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Author : Abdelhamid Ajbar
language : en
Publisher: CRC Press
Release Date : 2011-08-09
Dynamics Of The Chemostat written by Abdelhamid Ajbar and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-09 with Mathematics categories.
A ubiquitous tool in mathematical biology and chemical engineering, the chemostat often produces instabilities that pose safety hazards and adversely affect the optimization of bioreactive systems. Singularity theory and bifurcation diagrams together offer a useful framework for addressing these issues. Based on the authors’ extensive work in this field, Dynamics of the Chemostat: A Bifurcation Theory Approach explores the use of bifurcation theory to analyze the static and dynamic behavior of the chemostat. Introduction The authors first survey the major work that has been carried out on the stability of continuous bioreactors. They next present the modeling approaches used for bioreactive systems, the different kinetic expressions for growth rates, and tools, such as multiplicity, bifurcation, and singularity theory, for analyzing nonlinear systems. Application The text moves on to the static and dynamic behavior of the basic unstructured model of the chemostat for constant and variable yield coefficients as well as in the presence of wall attachment. It then covers the dynamics of interacting species, including pure and simple microbial competition, biodegradation of mixed substrates, dynamics of plasmid-bearing and plasmid-free recombinant cultures, and dynamics of predator–prey interactions. The authors also examine dynamics of the chemostat with product formation for various growth models, provide examples of bifurcation theory for studying the operability and dynamics of continuous bioreactor models, and apply elementary concepts of bifurcation theory to analyze the dynamics of a periodically forced bioreactor. Using singularity theory and bifurcation techniques, this book presents a cohesive mathematical framework for analyzing and modeling the macro- and microscopic interactions occurring in chemostats. The text includes models that describe the intracellular and operating elements of the bioreactive system. It also explains the mathematical theory behind the models.