Local Bifurcation and Symmetry
| Author | : A. Vanderbauwhede |
| Publisher | : |
| Total Pages | : 368 |
| Release | : 1982 |
| Genre | : Mathematics |
| ISBN | : |
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Global Bifurcation of Periodic Solutions with Symmetry
| Author | : Bernold Fiedler |
| Publisher | : Springer |
| Total Pages | : 151 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 3540391509 |
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This largely self-contained research monograph addresses the following type of questions. Suppose one encounters a continuous time dynamical system with some built-in symmetry. Should one expect periodic motions which somehow reflect this symmetry? And how would periodicity harmonize with symmetry? Probing into these questions leads from dynamics to topology, algebra, singularity theory, and to many applications. Within a global approach, the emphasis is on periodic motions far from equilibrium. Mathematical methods include bifurcation theory, transversality theory, and generic approximations. A new homotopy invariant is designed to study the global interdependence of symmetric periodic motions. Besides mathematical techniques, the book contains 5 largely nontechnical chapters. The first three outline the main questions, results and methods. A detailed discussion pursues theoretical consequences and open problems. Results are illustrated by a variety of applications including coupled oscillators and rotating waves: these links to such disciplines as theoretical biology, chemistry, fluid dynamics, physics and their engineering counterparts make the book directly accessible to a wider audience.
Local bifurcation and symmetry
| Author | : André L. Vanderbauwhede |
| Publisher | : |
| Total Pages | : 318 |
| Release | : 1980 |
| Genre | : |
| ISBN | : |
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Bifurcation, Symmetry and Patterns
| Author | : Jorge Buescu |
| Publisher | : Birkhäuser |
| Total Pages | : 215 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034879822 |
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The latest developments on both the theory and applications of bifurcations with symmetry. The text includes recent experimental work as well as new approaches to and applications of the theory to other sciences. It shows the range of dissemination of the work of Martin Golubitsky and Ian Stewart and its influence in modern mathematics at the same time as it contains work of young mathematicians in new directions. The range of topics includes mathematical biology, pattern formation, ergodic theory, normal forms, one-dimensional dynamics and symmetric dynamics.
Bifurcation and Symmetry
| Author | : BÖHMER |
| Publisher | : Birkhäuser |
| Total Pages | : 323 |
| Release | : 2013-03-08 |
| Genre | : Science |
| ISBN | : 3034875363 |
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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.
Encyclopedia of Systems Biology
| Author | : Werner Dubitzky |
| Publisher | : Springer |
| Total Pages | : 0 |
| Release | : 2013-06-05 |
| Genre | : Science |
| ISBN | : 9781441998620 |
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Systems biology refers to the quantitative analysis of the dynamic interactions among several components of a biological system and aims to understand the behavior of the system as a whole. Systems biology involves the development and application of systems theory concepts for the study of complex biological systems through iteration over mathematical modeling, computational simulation and biological experimentation. Systems biology could be viewed as a tool to increase our understanding of biological systems, to develop more directed experiments, and to allow accurate predictions. The Encyclopedia of Systems Biology is conceived as a comprehensive reference work covering all aspects of systems biology, in particular the investigation of living matter involving a tight coupling of biological experimentation, mathematical modeling and computational analysis and simulation. The main goal of the Encyclopedia is to provide a complete reference of established knowledge in systems biology – a ‘one-stop shop’ for someone seeking information on key concepts of systems biology. As a result, the Encyclopedia comprises a broad range of topics relevant in the context of systems biology. The audience targeted by the Encyclopedia includes researchers, developers, teachers, students and practitioners who are interested or working in the field of systems biology. Keeping in mind the varying needs of the potential readership, we have structured and presented the content in a way that is accessible to readers from wide range of backgrounds. In contrast to encyclopedic online resources, which often rely on the general public to author their content, a key consideration in the development of the Encyclopedia of Systems Biology was to have subject matter experts define the concepts and subjects of systems biology.
Dynamics, Bifurcation, and Symmetry
| Author | : Pascal Chossat |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 380 |
| Release | : 1994 |
| Genre | : Mathematics |
| ISBN | : |
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Summarizes the work of the European Bifurcation Theory Group after its first two years. The 28 papers discuss oscillator networks with the symmetry of the unit quaternion group, non- linear parabolic evolutions in unbounded domains, and symmetries and reversing symmetries in kicked systems. No index. Annotation copyright by Book News, Inc., Portland, OR
Dynamics, Bifurcation and Symmetry
| Author | : Pascal Chossat |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 355 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9401109567 |
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This book collects contributions to the conference" Dynamics, Bifurcation and Symmetry, new trends and new tools", which was held at the Institut d'Etudes Sci entifiques de Cargese (France), September 3-9, 1993. The first aim of this conference was to gather and summarize the work of the European Bifurcation Theory Group after two years of existence (the EBTG links european laboratories in five countries via an EC grant). Thanks to a NATO ARW grant, the conference developed into an international meeting on bifurcation theory and dynamical systems, with the partic ipation of leading specialists not only from Europe but also from overseas countries (Canada, USA, South America). It was a great satisfaction to notice the active, and quite enthusiastic participation of many young scientists. This is reflected in the present book for which many contributors are PhD students or post-doc researchers. Although several "big" themes (bifurcation with symmetry, low dimensional dynam ics, dynamics in EDP's, applications, . . . ) are present in these proceedings, we have divided the book into corresponding parts. In fact these themes overlap in most contributions, which seems to reflect a general tendancy in nonlinear science. I am very pleased to thank for their support the NATO International Exchange Scientific Program as well as the EEC Science Program, which made possible the suc cess of this conference.
Elements of Applied Bifurcation Theory
| Author | : Yuri Kuznetsov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 648 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 1475739788 |
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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.
Global Bifurcation of Periodic Solutions with Symmetry
| Author | : |
| Publisher | : |
| Total Pages | : 144 |
| Release | : 1988 |
| Genre | : Bifurcation theory |
| ISBN | : 9780387192345 |
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