Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Syste MS

The Institute for Mathematics & its Applications (IMA) devoted its 1997-1998 program to Emerging Applications of Dynamical Systems. Dynamical systems theory & related numerical algorithms provide powerful tools for studying the solution behavior of differential equations & mappings. In the past 25 years computational methods have been developed for calculating fixed points, limit cycles & 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 & connecting orbits, as well as the calculation 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 & their linear stability can be prohibitively expensive for large systems if attempted by simple direct methods. Several of the papers in this volume treat computational methods for low & 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 & unfolding of singular heteroclinic cycles. Other papers treat applications of dynamical systems computations in various scientific fields, such as biology, chemical engineering, fluid mechanics & mechanical engineering.Doedel, Eusebius is the author of 'Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Syste MS' with ISBN 9780387989709 and ISBN 0387989706.