Bifurcation And Chaos Analysis Algorithms Applications
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Bifurcation And Chaos Analysis Algorithms Applications
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Author : KÜPPER
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Bifurcation And Chaos Analysis Algorithms Applications written by KÜPPER and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This volume contains the proceedings of a conference held in Wiirzburg, August 20-24, 1990. The theme of the conference was Bifurcation and Chaos: Analysis, Algorithms, Ap plications. More than 100 scientists from 21 countries presented 80 contributions. Many of the results of the conference are described in the 49 refereed papers that follow. The conference was sponsored by the Deutsche Forschungsgemeinschaft, and by the Deutscher Akademischer Austauschdienst. We gratefully acknowledge the support from these agen cies. The science of nonlinear phenomena is evolving rapidly. Over the last 10 years, the emphasis has been gradually shifting. How trends vary may be seen by comparing these proceedings with previous ones, in particular with the conference held in Dortmund 1986 (proceedings published in ISNM 79). Concerning the range of phenomena, chaos has joined the bifurcation scenarios. As expected, the acceptance of chaos is less emotional among professionals, than it has been in some popular publications. A nalytical methods appear to have reached a state in which basic results of singularities, symmetry groups, or normal forms are everyday experience rather than exciting news. Similarly, numerical algorithms for frequent situations are now well established. Implemented in several packages, such algorithms have become standard means for attacking nonlinear problems. The sophisti cation that analytical and numerical methods have reached supports the vigorous trend to more and more applications. Pioneering equations as those named after Duffing, Van der Pol, or Lorenz, are no longer exclusively the state of art.
Bifurcation And Chaos Analysis Algorithms Applications
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Author : KÜPPER
language : en
Publisher: Birkhäuser
Release Date : 1991-04-01
Bifurcation And Chaos Analysis Algorithms Applications written by KÜPPER and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-04-01 with Mathematics categories.
This volume contains the proceedings of a conference held in Wiirzburg, August 20-24, 1990. The theme of the conference was Bifurcation and Chaos: Analysis, Algorithms, Ap plications. More than 100 scientists from 21 countries presented 80 contributions. Many of the results of the conference are described in the 49 refereed papers that follow. The conference was sponsored by the Deutsche Forschungsgemeinschaft, and by the Deutscher Akademischer Austauschdienst. We gratefully acknowledge the support from these agen cies. The science of nonlinear phenomena is evolving rapidly. Over the last 10 years, the emphasis has been gradually shifting. How trends vary may be seen by comparing these proceedings with previous ones, in particular with the conference held in Dortmund 1986 (proceedings published in ISNM 79). Concerning the range of phenomena, chaos has joined the bifurcation scenarios. As expected, the acceptance of chaos is less emotional among professionals, than it has been in some popular publications. A nalytical methods appear to have reached a state in which basic results of singularities, symmetry groups, or normal forms are everyday experience rather than exciting news. Similarly, numerical algorithms for frequent situations are now well established. Implemented in several packages, such algorithms have become standard means for attacking nonlinear problems. The sophisti cation that analytical and numerical methods have reached supports the vigorous trend to more and more applications. Pioneering equations as those named after Duffing, Van der Pol, or Lorenz, are no longer exclusively the state of art.
Practical Bifurcation And Stability Analysis
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Author : Rüdiger Seydel
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-14
Practical Bifurcation And Stability Analysis written by Rüdiger Seydel 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 2009-12-14 with Mathematics categories.
Probably the first book to describe computational methods for numerically computing steady state and Hopf bifurcations. Requiring only a basic knowledge of calculus, and using detailed examples, problems, and figures, this is an ideal textbook for graduate students.
Bifurcation And Symmetry
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Author : BÖHMER
language : en
Publisher: Birkhäuser
Release Date : 2013-03-08
Bifurcation And Symmetry written by BÖHMER and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-08 with Social Science categories.
Symmetry is a property which occurs throughout nature and it is therefore natural that symmetry should be considered when attempting to model nature. In many cases, these models are also nonlinear and it is the study of nonlinear symmetric models that has been the basis of much recent work. Although systematic studies of nonlinear problems may be traced back at least to the pioneering contributions of Poincare, this remains an area with challenging problems for mathematicians and scientists. Phenomena whose models exhibit both symmetry and nonlinearity lead to problems which are challenging and rich in complexity, beauty and utility. In recent years, the tools provided by group theory and representation theory have proven to be highly effective in treating nonlinear problems involving symmetry. By these means, highly complex situations may be decomposed into a number of simpler ones which are already understood or are at least easier to handle. In the realm of numerical approximations, the systematic exploitation of symmetry via group repre sentation theory is even more recent. In the hope of stimulating interaction and acquaintance with results and problems in the various fields of applications, bifurcation theory and numerical analysis, we organized the conference and workshop Bifurcation and Symmetry: Cross Influences between Mathematics and Applications during June 2-7,8-14, 1991 at the Philipps University of Marburg, Germany.
Practical Bifurcation And Stability Analysis
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Author : Rüdiger Seydel
language : en
Publisher: Springer
Release Date : 2012-05-03
Practical Bifurcation And Stability Analysis written by Rüdiger Seydel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-03 with Mathematics categories.
Probably the first book to describe computational methods for numerically computing steady state and Hopf bifurcations. Requiring only a basic knowledge of calculus, and using detailed examples, problems, and figures, this is an ideal textbook for graduate students.
The Graduate Student S Guide To Numerical Analysis 98
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Author : Mark Ainsworth
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Graduate Student S Guide To Numerical Analysis 98 written by Mark Ainsworth 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.
The Eighth EPSRC Numerical Analysis Summer School was held at the Uni versity of Leicester from the 5th to the 17th of July, 1998. This was the third Numerical Analysis Summer School to be held in Leicester. The previous meetings, in 1992 and 1994, had been carefully structured to ensure that each week had a coherent 'theme'. For the 1998 meeting, in order to widen the audience, we decided to relax this constraint. Speakers were chosen to cover what may appear, at first sight, to be quite diverse areas of numeri cal analysis. However, we were pleased with the extent to which the ideas cohered, and particularly enjoyed the discussions which arose from differing interpretations of those ideas. We would like to thank all six of our main speakers for the care which they took in the preparation and delivery of their lectures. In this volume we present their lecture notes in alphabetical rather than chronological order. Nick Higham, Alastair Spence and Nick Trefethen were the speakers in week 1, while Bernardo Cockburn, Stig Larsson and Bob Skeel were the speakers in week 2. Another new feature of this meeting compared to its predecessors was that we had 'invited seminars'. A numer of established academics based in the UK were asked to participate in the afternoon seminar program.
Numerical Bifurcation Analysis For Reaction Diffusion Equations
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Author : Zhen Mei
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Numerical Bifurcation Analysis For Reaction Diffusion Equations written by Zhen Mei 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.
Reaction-diffusion equations are typical mathematical models in biology, chemistry and physics. These equations often depend on various parame ters, e. g. temperature, catalyst and diffusion rate, etc. Moreover, they form normally a nonlinear dissipative system, coupled by reaction among differ ent substances. The number and stability of solutions of a reaction-diffusion system may change abruptly with variation of the control parameters. Cor respondingly we see formation of patterns in the system, for example, an onset of convection and waves in the chemical reactions. This kind of phe nomena is called bifurcation. Nonlinearity in the system makes bifurcation take place constantly in reaction-diffusion processes. Bifurcation in turn in duces uncertainty in outcome of reactions. Thus analyzing bifurcations is essential for understanding mechanism of pattern formation and nonlinear dynamics of a reaction-diffusion process. However, an analytical bifurcation analysis is possible only for exceptional cases. This book is devoted to nu merical analysis of bifurcation problems in reaction-diffusion equations. The aim is to pursue a systematic investigation of generic bifurcations and mode interactions of a dass of reaction-diffusion equations. This is realized with a combination of three mathematical approaches: numerical methods for con tinuation of solution curves and for detection and computation of bifurcation points; effective low dimensional modeling of bifurcation scenario and long time dynamics of reaction-diffusion equations; analysis of bifurcation sce nario, mode-interactions and impact of boundary conditions.
Numerical Solution Of The Incompressible Navier Stokes Equations
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Author : L. Quartapelle
language : en
Publisher: Birkhäuser
Release Date : 2013-03-07
Numerical Solution Of The Incompressible Navier Stokes Equations written by L. Quartapelle and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-07 with Social Science categories.
This book presents different formulations of the equations governing incompressible viscous flows, in the form needed for developing numerical solution procedures. The conditions required to satisfy the no-slip boundary conditions in the various formulations are discussed in detail. Rather than focussing on a particular spatial discretization method, the text provides a unitary view of several methods currently in use for the numerical solution of incompressible Navier-Stokes equations, using either finite differences, finite elements or spectral approximations. For each formulation, a complete statement of the mathematical problem is provided, comprising the various boundary, possibly integral, and initial conditions, suitable for any theoretical and/or computational development of the governing equations. The text is suitable for courses in fluid mechanics and computational fluid dynamics. It covers that part of the subject matter dealing with the equations for incompressible viscous flows and their determination by means of numerical methods. A substantial portion of the book contains new results and unpublished material.
Software Systems For Structural Optimization
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Author : H.R. Hörnlein
language : en
Publisher: Birkhäuser
Release Date : 2013-03-07
Software Systems For Structural Optimization written by H.R. Hörnlein and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-07 with Social Science categories.
Herbert Hornlein, Klaus Schittkowski The finite element method (FEM) has been used successfully for many years to simulate and analyse mechanical structural problems. The results are accepted or rejected by means of comparison of state variables (stresses, displacements, natural frequencies etc.) and user requirements. In further analyses the design variables will be updated until the user specifications are met and the design is feasible. This is the primary aim of the design process. On this set of feasible designs, the additional requirement given by an objective function (e.g. weight, stiffness, efficiency, etc.) defines the structural optimization problem. In recent years more and more finite element based analysis systems were ex tended and offer now optimization modules. They proceed from the design model as defined for structural analysis, to perform an internal adaption of design pa rameters based on formal mathematical methods. Despite of many common features, there are significant differences in the selected optimization strategy, the current implementation and the numerical results.
Hopf Bifurcation Analysis
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Author : Jorge L. Moiola
language : en
Publisher: World Scientific
Release Date : 1996
Hopf Bifurcation Analysis written by Jorge L. Moiola and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
This book is devoted to the frequency domain approach, for both regular and degenerate Hopf bifurcation analyses. Besides showing that the time and frequency domain approaches are in fact equivalent, the fact that many significant results and computational formulas obtained in the studies of regular and degenerate Hopf bifurcations from the time domain approach can be translated and reformulated into the corresponding frequency domain setting, and be reconfirmed and rediscovered by using the frequency domain methods, is also explained. The description of how the frequency domain approach can be used to obtain several types of standard bifurcation conditions for general nonlinear dynamical systems is given as well as is demonstrated a very rich pictorial gallery of local bifurcation diagrams for nonlinear systems under simultaneous variations of several system parameters. In conjunction with this graphical analysis of local bifurcation diagrams, the defining and nondegeneracy conditions for several degenerate Hopf bifurcations is presented. With a great deal of algebraic computation, some higher-order harmonic balance approximation formulas are derived, for analyzing the dynamical behavior in small neighborhoods of certain types of degenerate Hopf bifurcations that involve multiple limit cycles and multiple limit points of periodic solutions. In addition, applications in chemical, mechanical and electrical engineering as well as in biology are discussed. This book is designed and written in a style of research monographs rather than classroom textbooks, so that the most recent contributions to the field can be included with references.