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Bifurcate
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Download or read book Bifurcate written by Bernard Stiegler and published by Open Humanities Press. This book was released on 2021-12-08 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Imperfect Bifurcation in Structures and Materials by : Kiyohiro Ikeda
Download or read book Imperfect Bifurcation in Structures and Materials written by Kiyohiro Ikeda and published by Springer Science & Business Media. This book was released on 2002-05-31 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Singularities and Groups in Bifurcation Theory by : Martin Golubitsky
Download or read book Singularities and Groups in Bifurcation Theory written by Martin Golubitsky and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Methods of Bifurcation Theory by : S.-N. Chow
Download or read book Methods of Bifurcation Theory written by S.-N. Chow and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Elementary Stability and Bifurcation Theory by : G. Iooss
Download or read book Elementary Stability and Bifurcation Theory written by G. Iooss and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Topics in Stability and Bifurcation Theory by : David H. Sattinger
Download or read book Topics in Stability and Bifurcation Theory written by David H. Sattinger and published by Springer. This book was released on 2006-11-15 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Bifurcation Theory and Spatio-Temporal Pattern Formation by : Wayne Nagata
Download or read book Bifurcation Theory and Spatio-Temporal Pattern Formation written by Wayne Nagata and published by American Mathematical Soc.. This book was released on 2006-10-03 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Book Synopsis Elements of Applied Bifurcation Theory by : Yuri Kuznetsov
Download or read book Elements of Applied Bifurcation Theory written by Yuri Kuznetsov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Proceedings of the Academy of Natural Sciences of Philadelphia by :
Download or read book Proceedings of the Academy of Natural Sciences of Philadelphia written by and published by . This book was released on 1870 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis University of California Publications in American Archaeology and Ethnology by : Edward Winslow Gifford
Download or read book University of California Publications in American Archaeology and Ethnology written by Edward Winslow Gifford and published by . This book was released on 1922 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Host Bibliographic Record for Boundwith Item Barcode 30112124431161 and Others by :
Download or read book Host Bibliographic Record for Boundwith Item Barcode 30112124431161 and Others written by and published by . This book was released on 1922 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Bulletin of the Illinois State Museum of Natural History by : Illinois State Museum
Download or read book Bulletin of the Illinois State Museum of Natural History written by Illinois State Museum and published by . This book was released on 1894 with total page 900 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Pamphlets on Biology written by and published by . This book was released on 1896 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Dynamics of the Chemostat by : Abdelhamid Ajbar
Download or read book Dynamics of the Chemostat written by Abdelhamid Ajbar and published by CRC Press. This book was released on 2011-08-09 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Elements of Differentiable Dynamics and Bifurcation Theory by : David Ruelle
Download or read book Elements of Differentiable Dynamics and Bifurcation Theory written by David Ruelle and published by Elsevier. This book was released on 2014-05-10 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Global Bifurcation Theory and Hilbert’s Sixteenth Problem by : V. Gaiko
Download or read book Global Bifurcation Theory and Hilbert’s Sixteenth Problem written by V. Gaiko and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: On the 8th of August 1900 outstanding German mathematician David Hilbert delivered a talk "Mathematical problems" at the Second Interna tional Congress of Mathematicians in Paris. The talk covered practically all directions of mathematical thought of that time and contained a list of 23 problems which determined the further development of mathema tics in many respects (1, 119]. Hilbert's Sixteenth Problem (the second part) was stated as follows: Problem. To find the maximum number and to determine the relative position of limit cycles of the equation dy Qn(X, y) -= dx Pn(x, y)' where Pn and Qn are polynomials of real variables x, y with real coeffi cients and not greater than n degree. The study of limit cycles is an interesting and very difficult problem of the qualitative theory of differential equations. This theory was origi nated at the end of the nineteenth century in the works of two geniuses of the world science: of the Russian mathematician A. M. Lyapunov and of the French mathematician Henri Poincare. A. M. Lyapunov set forth and solved completely in the very wide class of cases a special problem of the qualitative theory: the problem of motion stability (154]. In turn, H. Poincare stated a general problem of the qualitative analysis which was formulated as follows: not integrating the differential equation and using only the properties of its right-hand sides, to give as more as possi ble complete information on the qualitative behaviour of integral curves defined by this equation (176].
Book Synopsis Numerical Continuation and Bifurcation in Nonlinear PDEs by : Hannes Uecker
Download or read book Numerical Continuation and Bifurcation in Nonlinear PDEs written by Hannes Uecker and published by SIAM. This book was released on 2021-08-19 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
