Numerical Continuation Methods For Dynamical Systems
DOWNLOAD eBooks
Download Numerical Continuation Methods For Dynamical Systems PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Numerical Continuation Methods For Dynamical Systems book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Numerical Continuation Methods For Dynamical Systems
DOWNLOAD eBooks
Author : Bernd Krauskopf
language : en
Publisher: Springer
Release Date : 2007-11-06
Numerical Continuation Methods For Dynamical Systems written by Bernd Krauskopf and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-06 with Science categories.
Path following in combination with boundary value problem solvers has emerged as a continuing and strong influence in the development of dynamical systems theory and its application. It is widely acknowledged that the software package AUTO - developed by Eusebius J. Doedel about thirty years ago and further expanded and developed ever since - plays a central role in the brief history of numerical continuation. This book has been compiled on the occasion of Sebius Doedel's 60th birthday. Bringing together for the first time a large amount of material in a single, accessible source, it is hoped that the book will become the natural entry point for researchers in diverse disciplines who wish to learn what numerical continuation techniques can achieve. The book opens with a foreword by Herbert B. Keller and lecture notes by Sebius Doedel himself that introduce the basic concepts of numerical bifurcation analysis. The other chapters by leading experts discuss continuation for various types of systems and objects and showcase examples of how numerical bifurcation analysis can be used in concrete applications. Topics that are treated include: interactive continuation tools, higher-dimensional continuation, the computation of invariant manifolds, and continuation techniques for slow-fast systems, for symmetric Hamiltonian systems, for spatially extended systems and for systems with delay. Three chapters review physical applications: the dynamics of a SQUID, global bifurcations in laser systems, and dynamics and bifurcations in electronic circuits.
Numerical Continuation Methods For Dynamical Systems
DOWNLOAD eBooks
Author : Bernd Krauskopf
language : en
Publisher: Springer
Release Date : 2007-07-26
Numerical Continuation Methods For Dynamical Systems written by Bernd Krauskopf and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-26 with Science categories.
Path following in combination with boundary value problem solvers has emerged as a continuing and strong influence in the development of dynamical systems theory and its application. It is widely acknowledged that the software package AUTO - developed by Eusebius J. Doedel about thirty years ago and further expanded and developed ever since - plays a central role in the brief history of numerical continuation. This book has been compiled on the occasion of Sebius Doedel's 60th birthday. Bringing together for the first time a large amount of material in a single, accessible source, it is hoped that the book will become the natural entry point for researchers in diverse disciplines who wish to learn what numerical continuation techniques can achieve. The book opens with a foreword by Herbert B. Keller and lecture notes by Sebius Doedel himself that introduce the basic concepts of numerical bifurcation analysis. The other chapters by leading experts discuss continuation for various types of systems and objects and showcase examples of how numerical bifurcation analysis can be used in concrete applications. Topics that are treated include: interactive continuation tools, higher-dimensional continuation, the computation of invariant manifolds, and continuation techniques for slow-fast systems, for symmetric Hamiltonian systems, for spatially extended systems and for systems with delay. Three chapters review physical applications: the dynamics of a SQUID, global bifurcations in laser systems, and dynamics and bifurcations in electronic circuits.
Numerical Methods For Bifurcations Of Dynamical Equilibria
DOWNLOAD eBooks
Author : Willy J. F. Govaerts
language : en
Publisher: SIAM
Release Date : 2000-01-01
Numerical Methods For Bifurcations Of Dynamical Equilibria written by Willy J. F. Govaerts and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-01 with Mathematics categories.
Numerical methods for the detection, computation, and continuation of equilibria and bifurcation points of equilibria of dynamical systems.
Dynamical Systems And Numerical Analysis
DOWNLOAD eBooks
Author : Andrew Stuart
language : en
Publisher: Cambridge University Press
Release Date : 1998-11-28
Dynamical Systems And Numerical Analysis written by Andrew Stuart 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 1998-11-28 with Mathematics categories.
The first three chapters contain the elements of the theory of dynamical systems and the numerical solution of initial-value problems. In the remaining chapters, numerical methods are formulated as dynamical systems and the convergence and stability properties of the methods are examined.
Numerical Continuation Methods
DOWNLOAD eBooks
Author : Eugene L. Allgower
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Numerical Continuation Methods written by Eugene L. Allgower 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.
Over the past fifteen years two new techniques have yielded extremely important contributions toward the numerical solution of nonlinear systems of equations. This book provides an introduction to and an up-to-date survey of numerical continuation methods (tracing of implicitly defined curves) of both predictor-corrector and piecewise-linear types. It presents and analyzes implementations aimed at applications to the computation of zero points, fixed points, nonlinear eigenvalue problems, bifurcation and turning points, and economic equilibria. Many algorithms are presented in a pseudo code format. An appendix supplies five sample FORTRAN programs with numerical examples, which readers can adapt to fit their purposes, and a description of the program package SCOUT for analyzing nonlinear problems via piecewise-linear methods. An extensive up-to-date bibliography spanning 46 pages is included. The material in this book has been presented to students of mathematics, engineering and sciences with great success, and will also serve as a valuable tool for researchers in the field.
Numerical Methods For Parameter Continuation Problems
DOWNLOAD eBooks
Author : Jonathan Pearce
language : en
Publisher:
Release Date : 2010
Numerical Methods For Parameter Continuation Problems written by Jonathan Pearce and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Continuation methods categories.
Handbook Of Dynamical Systems
DOWNLOAD eBooks
Author : B. Fiedler
language : en
Publisher: Gulf Professional Publishing
Release Date : 2002-02-21
Handbook Of Dynamical Systems written by B. Fiedler and has been published by Gulf Professional Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-02-21 with Science categories.
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.
Numerical Methods For Bifurcation Problems And Large Scale Dynamical Systems
DOWNLOAD eBooks
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.
Optimal Auxiliary Functions Method For Nonlinear Dynamical Systems
DOWNLOAD eBooks
Author : Vasile Marinca
language : en
Publisher: Springer Nature
Release Date : 2021-07-14
Optimal Auxiliary Functions Method For Nonlinear Dynamical Systems written by Vasile Marinca and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-14 with Technology & Engineering categories.
This book presents the optimal auxiliary functions method and applies it to various engineering problems and in particular in boundary layer problems. The cornerstone of the presented procedure is the concept of “optimal auxiliary functions” which are needed to obtain accurate results in an efficient way. Unlike other known analytic approaches, this procedure provides us with a simple but rigorous way to control and adjust the convergence of the solutions of nonlinear dynamical systems. The optimal auxiliary functions are depending on some convergence-control parameters whose optimal values are rigorously determined from mathematical point of view. The capital strength of our procedure is its fast convergence, since after only one iteration, we obtain very accurate analytical solutions which are very easy to be verified. Moreover, no simplifying hypothesis or assumptions are made. The book contains a large amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines, and many more. The book is a continuation of our previous books “Nonlinear Dynamical Systems in Engineering. Some Approximate Approaches”, Springer-2011 and “The Optimal Homotopy Asymptotic Method. Engineering Applications”, Springer-2015.
Applied Nonlinear Dynamics
DOWNLOAD eBooks
Author : Ali H. Nayfeh
language : en
Publisher: John Wiley & Sons
Release Date : 2008-11-20
Applied Nonlinear Dynamics written by Ali H. Nayfeh and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-20 with Science categories.
A unified and coherent treatment of analytical, computational and experimental techniques of nonlinear dynamics with numerous illustrative applications. Features a discourse on geometric concepts such as Poincaré maps. Discusses chaos, stability and bifurcation analysis for systems of differential and algebraic equations. Includes scores of examples to facilitate understanding.