Bifurcate PDF Download
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Author | : Bernard Stiegler |
Publisher | : Open Humanities Press |
Total Pages | : 328 |
Release | : 2021-12-08 |
Genre | : |
ISBN | : 9781785421228 |
Download Bifurcate Book in PDF, ePub and Kindle
The collective work that produced this book is based on the claim that today's destructive development model is reaching its ultimate limits, and that its toxicity, which is increasingly massive, manifest and multidimensional (medical, environmental, mental, epistemological, economic - accumulating pockets of insolvency, which become veritable oceans), is generated above all by the fact that the current industrial economy is based in every sector on an obsolete physical model - a mechanism that ignores the constraints of locality in biology and the entropic tendency in reticulated computational information. In these gravely perilous times, we must bifurcate: there is no alternative.
Author | : Kiyohiro Ikeda |
Publisher | : Springer Science & Business Media |
Total Pages | : 436 |
Release | : 2002-05-31 |
Genre | : Science |
ISBN | : 9780387954097 |
Download Imperfect Bifurcation in Structures and Materials Book in PDF, ePub and Kindle
Most physical systems lose or gain stability through bifurcation behavior. This book explains a series of experimentally found bifurcation phenomena by means of the methods of static bifurcation theory.
Author | : Martin Golubitsky |
Publisher | : Springer Science & Business Media |
Total Pages | : 480 |
Release | : 2013-11-27 |
Genre | : Mathematics |
ISBN | : 146125034X |
Download Singularities and Groups in Bifurcation Theory Book in PDF, ePub and Kindle
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.
Author | : Yuri Kuznetsov |
Publisher | : Springer Science & Business Media |
Total Pages | : 648 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 1475739788 |
Download Elements of Applied Bifurcation Theory Book in PDF, ePub and Kindle
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.
Author | : G. Iooss |
Publisher | : Springer Science & Business Media |
Total Pages | : 300 |
Release | : 2013-03-09 |
Genre | : Science |
ISBN | : 1468493361 |
Download Elementary Stability and Bifurcation Theory Book in PDF, ePub and Kindle
In its most general form bifurcation theory is a theory of equilibrium solutions of nonlinear equations. By equilibrium solutions we mean, for example, steady solutions, time-periodic solutions, and quasi-periodic solutions. The purpose of this book is to teach the theory of bifurcation of equilibrium solutions of evolution problems governed by nonlinear differential equations. We have written this book for the broaqest audience of potentially interested learners: engineers, biologists, chemists, physicists, mathematicians, econom ists, and others whose work involves understanding equilibrium solutions of nonlinear differential equations. To accomplish our aims, we have thought it necessary to make the analysis 1. general enough to apply to the huge variety of applications which arise in science and technology, and 2. simple enough so that it can be understood by persons whose mathe matical training does not extend beyond the classical methods of analysis which were popular in the 19th Century. Of course, it is not possible to achieve generality and simplicity in a perfect union but, in fact, the general theory is simpler than the detailed theory required for particular applications. The general theory abstracts from the detailed problems only the essential features and provides the student with the skeleton on which detailed structures of the applications must rest. It is generally believed that the mathematical theory of bifurcation requires some functional analysis and some of the methods of topology and dynamics.
Author | : David H. Sattinger |
Publisher | : Springer |
Total Pages | : 197 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540383336 |
Download Topics in Stability and Bifurcation Theory Book in PDF, ePub and Kindle
Author | : Richard H. Rand |
Publisher | : Springer Science & Business Media |
Total Pages | : 254 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461210607 |
Download Perturbation Methods, Bifurcation Theory and Computer Algebra Book in PDF, ePub and Kindle
Perturbation methods have always been an important tool for treating nonlinear differential equations. Now the drudgery associated with them has been eliminated! This book offers computer algebra (MACSYMA) programs which implement the most popular perturbation methods. Not only does this avoid the errors associated with hand computation, but the increase in efficiency permits more complicated problems to be tackled. This book is useful both for the beginner learning perturbation methods for the first time, as well as for the researcher. Methods covered include: Lindstedt's method, center manifolds, normal forms, two variable expansion method (method of multiple scales), averaging, Lie transforms and Liapunov-Schmidt reduction. For each method the book includes an introduction and some example problems solved both by hand and by machine. The examples feature common bifurcations such as the pitchfork and the Hopf. The MACSYMA code for each method is given and suggested exercises are provided at the end of each Chapter. An Appendix offers a brief introduction to MACSYMA.
Author | : J. E. Marsden |
Publisher | : Springer Science & Business Media |
Total Pages | : 420 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461263743 |
Download The Hopf Bifurcation and Its Applications Book in PDF, ePub and Kindle
The goal of these notes is to give a reasonahly com plete, although not exhaustive, discussion of what is commonly referred to as the Hopf bifurcation with applications to spe cific problems, including stability calculations. Historical ly, the subject had its origins in the works of Poincare [1] around 1892 and was extensively discussed by Andronov and Witt [1] and their co-workers starting around 1930. Hopf's basic paper [1] appeared in 1942. Although the term "Poincare Andronov-Hopf bifurcation" is more accurate (sometimes Friedrichs is also included), the name "Hopf Bifurcation" seems more common, so we have used it. Hopf's crucial contribution was the extension from two dimensions to higher dimensions. The principal technique employed in the body of the text is that of invariant manifolds. The method of Ruelle Takens [1] is followed, with details, examples and proofs added. Several parts of the exposition in the main text come from papers of P. Chernoff, J. Dorroh, O. Lanford and F. Weissler to whom we are grateful. The general method of invariant manifolds is common in dynamical systems and in ordinary differential equations: see for example, Hale [1,2] and Hartman [1]. Of course, other methods are also available. In an attempt to keep the picture balanced, we have included samples of alternative approaches. Specifically, we have included a translation (by L. Howard and N. Kopell) of Hopf's original (and generally unavailable) paper.
Author | : S.-N. Chow |
Publisher | : Springer Science & Business Media |
Total Pages | : 529 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461381592 |
Download Methods of Bifurcation Theory Book in PDF, ePub and Kindle
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.
Author | : Wayne Nagata |
Publisher | : American Mathematical Soc. |
Total Pages | : 186 |
Release | : 2006-10-03 |
Genre | : Mathematics |
ISBN | : 0821837257 |
Download Bifurcation Theory and Spatio-Temporal Pattern Formation Book in PDF, ePub and Kindle
Nonlinear dynamical systems and the formation of spatio-temporal patterns play an important role in current research on partial differential equations. This book contains articles on topics of current interest in applications of dynamical systems theory to problems of pattern formation in space and time. Topics covered include aspects of lattice dynamical systems, convection in fluid layers with large aspect ratios, mixed mode oscillations and canards, bacterial remediation of waste, gyroscopic systems, data clustering, and the second part of Hilbert's 16th problem. Most of the book consists of expository survey material, and so can serve as a source of convenient entry points to current research topics in nonlinear dynamics and pattern formation. This volume arose from a workshop held at the Fields Institute in December of 2003, honoring Professor William F. Langford's fundamental work on the occasion of his sixtieth birthday. Information for our distributors: Titles in this series are copublished with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).