Computational Methods In Bifurcation Theory And Dissipative Structures
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Computational Methods In Bifurcation Theory And Dissipative Structures
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Author : M. Kubicek
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Computational Methods In Bifurcation Theory And Dissipative Structures written by M. Kubicek 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 Science categories.
"Dissipative structures" is a concept which has recently been used in physics to discuss the formation of structures organized in space and/or time at the expense of the energy flowing into the system from the outside. The space-time structural organization of biological systems starting from the subcellular level up to the level of ecological systems, coherent structures in laser and of elastic stability in mechanics, instability in hydro plasma physics, problems dynamics leading to the development of turbulence, behavior of electrical networks and chemical reactors form just a short list of problems treated in this framework. Mathematical models constructed to describe these systems are usually nonlinear, often formed by complicated systems of algebraic, ordinary differ ential, or partial differential equations and include a number of character istic parameters. In problems of theoretical interest as well as engineering practice, we are concerned with the dependence of solutions on parameters and particularly with the values of parameters where qualitatively new types of solutions, e.g., oscillatory solutions, new stationary states, and chaotic attractors, appear (bifurcate). Numerical techniques to determine both bifurcation points and the depen dence of steady-state and oscillatory solutions on parameters are developed and discussed in detail in this text. The text is intended to serve as a working manual not only for students and research workers who are interested in dissipative structures, but also for practicing engineers who deal with the problems of constructing models and solving complicated nonlinear systems.
Computational Methods In Bifurcation Theory And Dissipative Structures
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Author : M Kubicek
language : en
Publisher:
Release Date : 1983-11-01
Computational Methods In Bifurcation Theory And Dissipative Structures written by M Kubicek and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-11-01 with categories.
Computational Methods In Bifurcation Theory And Dissipative Structures
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Author : Milan Kubíček
language : en
Publisher: Springer
Release Date : 1983
Computational Methods In Bifurcation Theory And Dissipative Structures written by Milan Kubíček and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Bifurcation theory categories.
Computational Methods In Bifurcation Theory And Dissipative Structures
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Author : Milan Kubicek
language : it
Publisher:
Release Date : 1983
Computational Methods In Bifurcation Theory And Dissipative Structures written by Milan Kubicek and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with categories.
Numerical Methods For Bifurcation Problems And Large Scale Dynamical Systems
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Author : Eusebius Doedel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Numerical Methods For Bifurcation Problems And Large Scale Dynamical Systems written by Eusebius Doedel 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 Institute for Mathematics and its Applications (IMA) devoted its 1997-1998 program to Emerging Applications of Dynamical Systems. Dynamical systems theory and related numerical algorithms provide powerful tools for studying the solution behavior of differential equations and mappings. In the past 25 years computational methods have been developed for calculating fixed points, limit cycles, and bifurcation points. A remaining challenge is to develop robust methods for calculating more complicated objects, such as higher- codimension bifurcations of fixed points, periodic orbits, and connecting orbits, as well as the calcuation of invariant manifolds. Another challenge is to extend the applicability of algorithms to the very large systems that result from discretizing partial differential equations. Even the calculation of steady states and their linear stability can be prohibitively expensive for large systems (e.g. 10_3- -10_6 equations) if attempted by simple direct methods. Several of the papers in this volume treat computational methods for low and high dimensional systems and, in some cases, their incorporation into software packages. A few papers treat fundamental theoretical problems, including smooth factorization of matrices, self -organized criticality, and unfolding of singular heteroclinic cycles. Other papers treat applications of dynamical systems computations in various scientific fields, such as biology, chemical engineering, fluid mechanics, and mechanical engineering.
Computational Modelling Of Bifurcations And Instabilities In Fluid Dynamics
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Author : Alexander Gelfgat
language : en
Publisher: Springer
Release Date : 2018-07-06
Computational Modelling Of Bifurcations And Instabilities In Fluid Dynamics written by Alexander Gelfgat and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-06 with Technology & Engineering categories.
Instabilities of fluid flows and the associated transitions between different possible flow states provide a fascinating set of problems that have attracted researchers for over a hundred years. This book addresses state-of-the-art developments in numerical techniques for computational modelling of fluid instabilities and related bifurcation structures, as well as providing comprehensive reviews of recently solved challenging problems in the field.
Chaotic Behaviour Of Deterministic Dissipative Systems
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Author : Milos Marek
language : en
Publisher: Cambridge University Press
Release Date : 1995-07-20
Chaotic Behaviour Of Deterministic Dissipative Systems written by Milos Marek and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-07-20 with Science categories.
This graduate text surveys both the theoretical and experimental aspects of deterministic chaotic behaviour.
Continuation Techniques And Bifurcation Problems
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Author : MITTELMANN
language : en
Publisher: Birkhäuser
Release Date : 2013-11-21
Continuation Techniques And Bifurcation Problems written by MITTELMANN and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-21 with Social Science categories.
The analysis of parameter-dependent nonlinear has received much attention in recent years. Numerical continuation techniques allow the efficient computation of solution branches in a one-parameter problem. In many cases continuation procedures are used as part of a more complete analysis of a nonlinear problem, based on bifurcation theory and singularity theory. These theories contribute to the understanding of many nonlinear phenomena in nature and they form the basis for various analytical and numerical tools, which provide qualitative and quantitative results about nonlinear systems. In this issue we have collected a number of papers dealing with continuation techniques and bifurcation problems. Readers familiar with the notions of continuation and bifurcation will find recent research results addressing a variety of aspects in this issue. Those who intend to learn about the field or a specific topic in it may find it useful to first consult earlier literature on the numerical treatment of these problems together with some theoretical background. The papers in this issue fall naturally into different groups.
Fundamentals Of Dynamical Systems And Bifurcation Theory
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Author : Milan Medved̕
language : en
Publisher: CRC Press
Release Date : 1992-05-21
Fundamentals Of Dynamical Systems And Bifurcation Theory written by Milan Medved̕ and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-05-21 with Mathematics categories.
This graduate level text explains the fundamentals of the theory of dynamical systems. After reading it you will have a good enough understanding of the area to study the extensive literature on dynamical systems. The book is self contained, as all the essential definitions and proofs are supplied, as are useful references: all the reader needs is a knowledge of basic mathematical analysis, algebra and topology. However, the first chapter contains an explanation of some of the methods of differential topology an understanding of which is essential to the theory of dynamical systems. A clear introduction to the field, which is equally useful for postgraduates in the natural sciences, engineering and economics.
Determination Of Complex Reaction Mechanisms
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Author : John Ross
language : en
Publisher: Oxford University Press
Release Date : 2006
Determination Of Complex Reaction Mechanisms written by John Ross and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Science categories.
In a chemical system with many chemical species several questions can be asked: what species react with other species: in what temporal order: and with what results? These questions have been asked for over one hundred years about simple and complex chemical systems, and the answers constitute the macroscopic reaction mechanism. In Determination of Complex Reaction Mechanisms authors John Ross, Igor Schreiber, and Marcel Vlad present several systematic approaches for obtaining information on the causal connectivity of chemical species, on correlations of chemical species, on the reaction pathway, and on the reaction mechanism.Basic pulse theory is demonstrated and tested in an experiment on glycolysis. In a second approach, measurements on time series of concentrations are used to construct correlation functions and a theory is developed which shows that from these functions information may be inferred on the reaction pathway, the reaction mechanism, and the centers of control in that mechanism. A third approach is based on application of genetic algorithm methods to the study of the evolutionary development of a reaction mechanism, to the attainment given goals in a mechanism, and to the determination of a reaction mechanism and rate coefficients by comparison with experiment. Responses of non-linear systems to pulses or other perturbations are analyzed, and mechanisms of oscillatory reactions are presented in detail. The concluding chapters give an introduction to bioinformatics and statistical methods for determining reaction mechanisms.