Bifurcation Symmetry And Patterns

Author : Jorge Buescu,Paulo M.S.T. de Castro,Ana Paula Dias,Isabel S. Labouriau
Publisher : Birkhäuser
Page : 215 pages
File Size : 45,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034879828

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Bifurcation, Symmetry and Patterns by Jorge Buescu,Paulo M.S.T. de Castro,Ana Paula Dias,Isabel S. Labouriau Pdf

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.

Author : Iuliana Oprea,Gerhard Dangelmayr
Publisher : World Scientific
Page : 405 pages
File Size : 47,6 Mb
Release : 2004-11-17
Category : Science
ISBN : 9789814482097

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Dynamics And Bifurcation Of Patterns In Dissipative Systems by Iuliana Oprea,Gerhard Dangelmayr Pdf

Understanding the spontaneous formation and dynamics of spatiotemporal patterns in dissipative nonequilibrium systems is one of the major challenges in nonlinear science. This collection of expository papers and advanced research articles, written by leading experts, provides an overview of the state of the art. The topics include new approaches to the mathematical characterization of spatiotemporal complexity, with special emphasis on the role of symmetry, as well as analysis and experiments of patterns in a remarkable variety of applied fields such as magnetoconvection, liquid crystals, granular media, Faraday waves, multiscale biological patterns, visual hallucinations, and biological pacemakers. The unitary presentations, guiding the reader from basic fundamental concepts to the most recent research results on each of the themes, make the book suitable for a wide audience.

Author : Rebecca B. Hoyle
Publisher : Cambridge University Press
Page : 440 pages
File Size : 53,8 Mb
Release : 2006-03-17
Category : Mathematics
ISBN : 0521817501

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Pattern Formation by Rebecca B. Hoyle Pdf

Fully illustrated mathematical guide to pattern formation. Includes instructive exercises and examples.

Author : John M. Chadam,Fields Institute for Research in Mathematical Sciences
Publisher : American Mathematical Soc.
Page : 369 pages
File Size : 40,8 Mb
Release : 1996
Category : MATHEMATICS
ISBN : 9780821802564

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Pattern Formation: Symmetry Methods and Applications by John M. Chadam,Fields Institute for Research in Mathematical Sciences Pdf

This volume contains the proceedings of two related workshops held at The Fields Institute in February and March 1993. The workshops were an integral part of the thematic year in Dynamical Systems and Bifurcation Theory held during the 1992-1993 academic year. This volume covers the full spectrum of research involved in combining symmetry methods with dynamical systems and bifurcation theory, from the development of the mathematical theory in order to understand the underlying mechanisms to the application of this new mathematical theory, to partial differential equation models of realistic ph.

Author : Kiyohiro Ikeda,Kazuo Murota
Publisher : Springer Nature
Page : 590 pages
File Size : 51,5 Mb
Release : 2019-09-25
Category : Science
ISBN : 9783030214739

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Imperfect Bifurcation in Structures and Materials by Kiyohiro Ikeda,Kazuo Murota Pdf

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 : Gerhard Dangelmayr,Iuliana Oprea
Publisher : World Scientific
Page : 405 pages
File Size : 54,7 Mb
Release : 2004
Category : Mathematics
ISBN : 9789812567840

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Dynamics and Bifurcation of Patterns in Dissipative Systems by Gerhard Dangelmayr,Iuliana Oprea Pdf

Understanding the spontaneous formation and dynamics of spatiotemporal patterns in dissipative nonequilibrium systems is one of the major challenges in nonlinear science. This collection of expository papers and advanced research articles, written by leading experts, provides an overview of the state of the art. The topics include new approaches to the mathematical characterization of spatiotemporal complexity, with special emphasis on the role of symmetry, as well as analysis and experiments of patterns in a remarkable variety of applied fields such as magnetoconvection, liquid crystals, granular media, Faraday waves, multiscale biological patterns, visual hallucinations, and biological pacemakers. The unitary presentations, guiding the reader from basic fundamental concepts to the most recent research results on each of the themes, make the book suitable for a wide audience.

Author : Martin Golubitsky,Ian Stewart
Publisher : Birkhäuser
Page : 325 pages
File Size : 53,7 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9783034881678

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The Symmetry Perspective by Martin Golubitsky,Ian Stewart Pdf

The framework of ‘symmetry’ provides an important route between the abstract theory and experimental observations. The book applies symmetry methods to dynamical systems, focusing on bifurcation and chaos theory. Its exposition is organized around a wide variety of relevant applications. From the reviews: "[The] rich collection of examples makes the book...extremely useful for motivation and for spreading the ideas to a large Community."--MATHEMATICAL REVIEWS

Author : Kiyohiro Ikeda,Kazuo Murota
Publisher : CRC Press
Page : 278 pages
File Size : 43,5 Mb
Release : 2021-12-30
Category : Mathematics
ISBN : 9781000508574

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Bifurcation and Buckling in Structures by Kiyohiro Ikeda,Kazuo Murota Pdf

Bifurcation and Buckling in Structures describes the theory and analysis of bifurcation and buckling in structures. Emphasis is placed on a general procedure for solving nonlinear governing equations and an analysis procedure related to the finite-element method. Simple structural examples using trusses, columns, and frames illustrate the principles. Part I presents fundamental issues such as the general mathematical framework for bifurcation and buckling, procedures for the buckling load/mode analyses, and numerical analysis procedures to trace the solution curves and switch to bifurcation solutions. Advanced topics include asymptotic theory of bifurcation and bifurcation theory of symmetric systems. Part II deals with buckling of perfect and imperfect structures. An overview of the member buckling of columns and beams is provided, followed by the buckling analysis of truss and frame structures. The worst and random imperfections are studied as advanced topics. An extensive review of the history of buckling is presented. This text is ideal for advanced undergraduate and graduate students in engineering and applied mathematics. To assist readers, problems are listed at the end of each chapter, and their answers are given at the end of the book. Kiyohiro Ikeda is Professor Emeritus at Tohoku University, Japan. Kazuo Murota is a Project Professor at the Institute of Statistical Mathematics, Japan, as well as Professor Emeritus at the University of Tokyo, Kyoto University, and Tokyo Metropolitan University, Japan.

Author : Martin Golubitsky ,Ian Stewart
Publisher : SIAM
Page : 867 pages
File Size : 49,7 Mb
Release : 2023-04-24
Category : Mathematics
ISBN : 9781611977332

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Dynamics and Bifurcation in Networks by Martin Golubitsky ,Ian Stewart Pdf

In recent years, there has been an explosion of interest in network-based modeling in many branches of science. This book synthesizes some of the common features of many such models, providing a general framework analogous to the modern theory of nonlinear dynamical systems. How networks lead to behavior not typical in a general dynamical system and how the architecture and symmetry of the network influence this behavior are the book’s main themes. Dynamics and Bifurcation in Networks: Theory and Applications of Coupled Differential Equations is the first book to describe the formalism for network dynamics developed over the past 20 years. In it, the authors introduce a definition of a network and the associated class of “admissible” ordinary differential equations, in terms of a directed graph whose nodes represent component dynamical systems and whose arrows represent couplings between these systems. They also develop connections between network architecture and the typical dynamics and bifurcations of these equations and discuss applications of this formalism to various areas of science, including gene regulatory networks, animal locomotion, decision-making, homeostasis, binocular rivalry, and visual illusions. This book will be of interest to scientific researchers in any area that uses network models, which includes many parts of biology, physics, chemistry, computer science, electrical and electronic engineering, psychology, and sociology.

Author : Kiyohiro Ikeda,Kazuo Murota
Publisher : Springer Science & Business Media
Page : 326 pages
File Size : 42,8 Mb
Release : 2013-11-08
Category : Technology & Engineering
ISBN : 9784431542582

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Bifurcation Theory for Hexagonal Agglomeration in Economic Geography by Kiyohiro Ikeda,Kazuo Murota Pdf

This book contributes to an understanding of how bifurcation theory adapts to the analysis of economic geography. It is easily accessible not only to mathematicians and economists, but also to upper-level undergraduate and graduate students who are interested in nonlinear mathematics. The self-organization of hexagonal agglomeration patterns of industrial regions was first predicted by the central place theory in economic geography based on investigations of southern Germany. The emergence of hexagonal agglomeration in economic geography models was envisaged by Krugman. In this book, after a brief introduction of central place theory and new economic geography, the missing link between them is discovered by elucidating the mechanism of the evolution of bifurcating hexagonal patterns. Pattern formation by such bifurcation is a well-studied topic in nonlinear mathematics, and group-theoretic bifurcation analysis is a well-developed theoretical tool. A finite hexagonal lattice is used to express uniformly distributed places, and the symmetry of this lattice is expressed by a finite group. Several mathematical methodologies indispensable for tackling the present problem are gathered in a self-contained manner. The existence of hexagonal distributions is verified by group-theoretic bifurcation analysis, first by applying the so-called equivariant branching lemma and next by solving the bifurcation equation. This book offers a complete guide for the application of group-theoretic bifurcation analysis to economic agglomeration on the hexagonal lattice.

Author : Zeljko Dimitrije Cupic,Annette F. Taylor,Dezso Horvath,Marek Orlik,Irving Robert Epstein
Publisher : Frontiers Media SA
Page : 133 pages
File Size : 55,8 Mb
Release : 2021-06-29
Category : Science
ISBN : 9782889669226

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Advances in Oscillating Reactions by Zeljko Dimitrije Cupic,Annette F. Taylor,Dezso Horvath,Marek Orlik,Irving Robert Epstein Pdf

Author : Pascal Chossat
Publisher : Springer Science & Business Media
Page : 355 pages
File Size : 43,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401109567

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Dynamics, Bifurcation and Symmetry by Pascal Chossat Pdf

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.

Author : Mike Field
Publisher : World Scientific
Page : 493 pages
File Size : 55,7 Mb
Release : 2007
Category : Mathematics
ISBN : 9781860948282

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Dynamics and Symmetry by Mike Field Pdf

This book contains the first systematic exposition of the global and local theory of dynamics equivariant with respect to a (compact) Lie group. Aside from general genericity and normal form theorems on equivariant bifurcation, it describes many general families of examples of equivariant bifurcation and includes a number of novel geometric techniques, in particular, equivariant transversality. This important book forms a theoretical basis of future work on equivariant reversible and Hamiltonian systems.This book also provides a general and comprehensive introduction to codimension one equivariant bifurcation theory. In particular, it includes the bifurcation theory developed with Roger Richardson on subgroups of reflection groups and the Maximal Isotropy Subgroup Conjecture. A number of general results are also given on the global theory. Introductory material on groups, representations and G-manifolds are covered in the first three chapters of the book. In addition, a self-contained introduction of equivariant transversality is given, including necessary results on stratifications as well as results on equivariant jet transversality developed by Edward Bierstone.

Author : A. Van Harten,A. Doelman
Publisher : Taylor & Francis
Page : 350 pages
File Size : 51,8 Mb
Release : 2022-09-16
Category : Mathematics
ISBN : 9781351428262

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Nonlinear Dynamics and Pattern Formation in the Natural Environment by A. Van Harten,A. Doelman Pdf

This Research Note aims to provide an insight into recent developments in the theory of pattern formation. In the last decade there has been considerable progress in this field, both from a theoretical and a practical point of view. Recent mathematical developments concern the study of the nonlinear stability of systems at near-critical conditions by an appropriate system of modulation equations. The complexity of the original problem can be reduced drastically by this approximation. Moreover, it provides unifying point of view for a wide range of problems. New applications of the theory arise in a multitude of scientific areas such as hydrodynamics, reaction-diffusion problems, oceanography, meteorology, combustion, geophysical and biological morphodynamics and semi-conductors.This book is intended to show the interactions between the mathematical theory of nonlinear dynamics and the study of pattern generating phenomena in the natural environment. There is an intimate relationship between new insights in the mathematical aspects of nonlinear pattern formation and the comprehension of such phenomena. Therefore there are two partly overlapping main themes: one in which the emphasis is on generally applicable mathematical theories and techniques and one in which the phenomenology of pattern evolution in various areas is discussed.The book comprises 19 contributions by experts in the field. Although the emphasis changes considerably from paper to paper, in each contribution the same two themes are present; all the authors have aimed to achieve a suitable balance between the mathematical theory and the physical phenomena.

Author : Visarath In,Antonio Palacios
Publisher : Springer
Page : 406 pages
File Size : 48,9 Mb
Release : 2017-09-05
Category : Technology & Engineering
ISBN : 9783662555453

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Symmetry in Complex Network Systems by Visarath In,Antonio Palacios Pdf

This book bridges the current gap between the theory of symmetry-based dynamics and its application to model and analyze complex systems. As an alternative approach, the authors use the symmetry of the system directly to formulate the appropriate models, and also to analyze the dynamics. Complex systems with symmetry arise in a wide variety of fields, including communication networks, molecular dynamics, manufacturing businesses, ecosystems, underwater vehicle dynamics, celestial and spacecraft dynamics and continuum mechanics. A general approach for their analysis has been to derive a detailed model of their individual parts, connect the parts and note that the system contains some sort of symmetry, then attempt to exploit this symmetry in order to simplify numerical computations. This approach can result in highly complicated models that are difficult to analyze even numerically. The alternative approach, while nonstandard, is not entirely new among the mathematics community. However, there is much less familiarity with the techniques of symmetry-breaking bifurcation, as they apply to the engineering, design and fabrication, of complex systems, in particular, nonlinear sensor devices with special emphasis on the conceptualization and development of new technologies of magnetic sensors such as fluxgate magnetometers and SQUID (Superconducting Quantum Interference Devices), E-- (electric-field) sensors, and communication and navigation systems that require multiple frequencies of operation, such as radar and antenna devices as well as gyroscopic systems.