Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems write by Eusebius Doedel. This book was released on 2000-03-17. Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems available in PDF, EPUB and Kindle.
Numerical Methods for Bifurcation Problems and Large-scale Dynamical Systems
Numerical Methods for Bifurcation Problems and Large-scale Dynamical Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Numerical Methods for Bifurcation Problems and Large-scale Dynamical Systems write by Eusebius Doedel. This book was released on 2000. Numerical Methods for Bifurcation Problems and Large-scale Dynamical Systems available in PDF, EPUB and Kindle. 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 theoreti
Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems
Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems write by Eusebius Doedel. This book was released on 2012-12-06. Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems available in PDF, EPUB and Kindle. 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.
Numerical Methods for Bifurcations of Dynamical Equilibria
Numerical Methods for Bifurcations of Dynamical Equilibria - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Numerical Methods for Bifurcations of Dynamical Equilibria write by Willy J. F. Govaerts. This book was released on 2000-01-01. Numerical Methods for Bifurcations of Dynamical Equilibria available in PDF, EPUB and Kindle. Dynamical systems arise in all fields of applied mathematics. The author focuses on the description of numerical methods for the detection, computation, and continuation of equilibria and bifurcation points of equilibria of dynamical systems. This subfield has the particular attraction of having links with the geometric theory of differential equations, numerical analysis, and linear algebra.
Numerical Continuation Methods for Dynamical Systems
Numerical Continuation Methods for Dynamical Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Numerical Continuation Methods for Dynamical Systems write by Bernd Krauskopf. This book was released on 2007-11-06. Numerical Continuation Methods for Dynamical Systems available in PDF, EPUB and Kindle. 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.
