Download or read book An Application of the Generalized Morse Index to Travelling Wave Solutions of a Competitive Reaction Diffusion Model written by Charles C. Conley and published by . This book was released on 1980 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: The existence of travelling wave solutions of a diffusion reaction-system is studied via the generalized Morse index of isolated invariant sets. This index theory is analogous to degree theory, and the method of proof follows lines familiar from the latter theory. The equations in question are 'deformed' to a 'standard' system where the index can be easily computed, and the existence theorem follows from the 'non-triviality' of the index. The index theory has been described in other papers; here the main job is to construct 'isolating neighborhoods' which are analogous (in the degree theory) to open sets with no critical points on the boundary. Some novel means of location such neighborhoods are described.
Download or read book Shock Waves and Reaction Diffusion Equations written by Joel Smoller and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: . . . the progress of physics will to a large extent depend on the progress of nonlinear mathe matics, of methods to solve nonlinear equations . . . and therefore we can learn by comparing different nonlinear problems. WERNER HEISENBERG I undertook to write this book for two reasons. First, I wanted to make easily available the basics of both the theory of hyperbolic conservation laws and the theory of systems of reaction-diffusion equations, including the generalized Morse theory as developed by C. Conley. These important subjects seem difficult to learn since the results are scattered throughout the research journals. 1 Second, I feel that there is a need to present the modern methods and ideas in these fields to a wider audience than just mathe maticians. Thus, the book has some rather sophisticated aspects to it, as well as certain textbook aspects. The latter serve to explain, somewhat, the reason that a book with the title Shock Waves and Reaction-Diffusion Equations has the first nine chapters devoted to linear partial differential equations. More precisely, I have found from my classroom experience that it is far easier to grasp the subtleties of nonlinear partial differential equations after one has an understanding of the basic notions in the linear theory. This book is divided into four main parts: linear theory, reaction diffusion equations, shock wave theory, and the Conley index, in that order. Thus, the text begins with a discussion of ill-posed problems.
Download or read book Wave Asymptotics written by P. A. Martin and published by Cambridge University Press. This book was released on 1992-05-29 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains papers by distinguished researchers in fluid mechanics and asymptotics. The papers collected here outline the development of these topics.
Download or read book Traveling Wave Solutions of Parabolic Systems written by A. I. Volpert and published by American Mathematical Soc.. This book was released on with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of travelling waves described by parabolic equations and systems is a rapidly developing branch of modern mathematics. This book presents a general picture of current results about wave solutions of parabolic systems, their existence, stability, and bifurcations. With introductory material accessible to non-mathematicians and a nearly complete bibliography of about 500 references, this book is an excellent resource on the subject.
Download or read book Travelling Wave Solutions of Diffusive Volterra lotka Interaction Equations written by Steven Ray Dunbar and published by . This book was released on 1981 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Handbook of Dynamical Systems written by B. Fiedler and published by Gulf Professional Publishing. This book was released on 2002-02-21 with total page 1099 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook is volume II in a series collecting mathematical state-of-the-art surveys in the field of dynamical systems. Much of this field has developed from interactions with other areas of science, and this volume shows how concepts of dynamical systems further the understanding of mathematical issues that arise in applications. Although modeling issues are addressed, the central theme is the mathematically rigorous investigation of the resulting differential equations and their dynamic behavior. However, the authors and editors have made an effort to ensure readability on a non-technical level for mathematicians from other fields and for other scientists and engineers. The eighteen surveys collected here do not aspire to encyclopedic completeness, but present selected paradigms. The surveys are grouped into those emphasizing finite-dimensional methods, numerics, topological methods, and partial differential equations. Application areas include the dynamics of neural networks, fluid flows, nonlinear optics, and many others. While the survey articles can be read independently, they deeply share recurrent themes from dynamical systems. Attractors, bifurcations, center manifolds, dimension reduction, ergodicity, homoclinicity, hyperbolicity, invariant and inertial manifolds, normal forms, recurrence, shift dynamics, stability, to namejust a few, are ubiquitous dynamical concepts throughout the articles.
Download or read book Nonlinear Problems Present and Future written by A. Bishop and published by Elsevier. This book was released on 1982-01-01 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Problems: Present and Future
Download or read book ICIAM 91 written by Robert E. O'Malley and published by SIAM. This book was released on 1992-01-01 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings -- Computer Arithmetic, Algebra, OOP.
Download or read book Viscous Profiles and Numerical Methods for Shock Waves written by Michael Shearer and published by SIAM. This book was released on 1991-01-01 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: One strongly represented theme is the power of ideas from dynamical systems that are being adapted and developed in the context of shock waves.
Download or read book Non Linear Analysis and Boundary Value Problems for Ordinary Differential Equations written by F. Zanolin and published by Springer. This book was released on 2014-05-04 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: The area covered by this volume represents a broad choice of some interesting research topics in the field of dynamical systems and applications of nonlinear analysis to ordinary and partial differential equations. The contributed papers, written by well known specialists, make this volume a useful tool both for the experts (who can find recent and new results) and for those who are interested in starting a research work in one of these topics (who can find some updated and carefully presented papers on the state of the art of the corresponding subject).
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1981 with total page 1370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Download or read book Competition and Cooperation in Neural Nets written by S. Amari and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: The human brain, wi th its hundred billion or more neurons, is both one of the most complex systems known to man and one of the most important. The last decade has seen an explosion of experimental research on the brain, but little theory of neural networks beyond the study of electrical properties of membranes and small neural circuits. Nonetheless, a number of workers in Japan, the United States and elsewhere have begun to contribute to a theory which provides techniques of mathematical analysis and computer simulation to explore properties of neural systems containing immense numbers of neurons. Recently, it has been gradually recognized that rather independent studies of the dynamics of pattern recognition, pattern format::ion, motor control, self-organization, etc. , in neural systems do in fact make use of common methods. We find that a "competition and cooperation" type of interaction plays a fundamental role in parallel information processing in the brain. The present volume brings together 23 papers presented at a U. S. -Japan Joint Seminar on "Competition and Cooperation in Neural Nets" which was designed to catalyze better integration of theory and experiment in these areas. It was held in Kyoto, Japan, February 15-19, 1982, under the joint sponsorship of the U. S. National Science Foundation and the Japan Society for the Promotion of Science. Participants included brain theorists, neurophysiologists, mathematicians, computer scientists, and physicists. There are seven papers from the U. S.
Download or read book Shock Waves and Reaction Diffusion Equations written by Joel Smoller and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt: For this edition, a number of typographical errors and minor slip-ups have been corrected. In addition, following the persistent encouragement of Olga Oleinik, I have added a new chapter, Chapter 25, which I titled "Recent Results." This chapter is divided into four sections, and in these I have discussed what I consider to be some of the important developments which have come about since the writing of the first edition. Section I deals with reaction-diffusion equations, and in it are described both the work of C. Jones, on the stability of the travelling wave for the Fitz-Hugh-Nagumo equations, and symmetry-breaking bifurcations. Section II deals with some recent results in shock-wave theory. The main topics considered are L. Tartar's notion of compensated compactness, together with its application to pairs of conservation laws, and T.-P. Liu's work on the stability of viscous profiles for shock waves. In the next section, Conley's connection index and connection matrix are described; these general notions are useful in con structing travelling waves for systems of nonlinear equations. The final sec tion, Section IV, is devoted to the very recent results of C. Jones and R. Gardner, whereby they construct a general theory enabling them to locate the point spectrum of a wide class of linear operators which arise in stability problems for travelling waves. Their theory is general enough to be applica ble to many interesting reaction-diffusion systems.
Download or read book Bibliography for Dynamical Systems written by Kenichi Shiraiwa and published by . This book was released on 1985 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dynamical Systems written by Ludwig Arnold and published by Springer. This book was released on 2006-11-14 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the lecture notes written by the four principal speakers at the C.I.M.E. session on Dynamical Systems held at Montecatini, Italy in June 1994. The goal of the session was to illustrate how methods of dynamical systems can be applied to the study of ordinary and partial differential equations. Topics in random differential equations, singular perturbations, the Conley index theory, and non-linear PDEs were discussed. Readers interested in asymptotic behavior of solutions of ODEs and PDEs and familiar with basic notions of dynamical systems will wish to consult this text.
Download or read book Conley Index Theory written by Konstantin Michael Mischaikow and published by . This book was released on 1999 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book MRC Technical Summary Report written by University of Wisconsin--Madison. Mathematics Research Center and published by . This book was released on 1980 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt:
