This IMA Volume in Mathematics and its Applications NUMERICAL METHODS FOR BIFURCATION PROBLEMS AND LARGE-SCALE DYNAMICAL SYSTEMS is based on the combined proceedings of two workshops devoted to compu­ tational issues. The workshops were an integral part of the 1997-98 IMA program on "EMERGING APPLICATIONS OF DYNAMICAL SYSTEMS." I would like to thank Donald G. Aronson, University of Minnesota (Mathematics); Wolf-Juergen Beyn, Universitaet Bielefeld (Fakultaet fuer Mathematik); Eusebius Doedel, California Institute of Technology (Applied Mathematics); Bernold Fiedler, Free University of Berlin (Mathematics); H.B. Keller, Caltech (Applied Mathematics); Yannis Kevrekidis, Princeton University (Chemical Enginering); Jens Lorenz, University of New Mex­ ico (Mathematics and Statistics); Edriss S. Titi, University of California (Mathematics); Laurette S. Tuckerman, Laboratoire d'Informatique pour la Mecanique et les Sciences de l'Ingenieur (LIMSI) for their excellent work as organizers of the meeting. Special appreciation to Eusebius Doedel and Laurette S. Tuckerman for serving as editors of the proceedings. I also take this opportunity to thank the National Science Foundation (NSF), and the National Security Agency (NSA), whose financial support made the workshop possible.

Dynamical systems theory and related numerical algorithms provide powerful tools for studying the solution behavior of differential equations and mappings. The papers in this volume are based on lectures given at the first two workshops held as part of the 1997- 1998 IMA Academic Year on Emerging Applications of Dynamical Systems. The first workshop concentrated on complex computational issues in dynamical systems. The second workshop addressed the development and application of special iterative methods for large scale systems. It also considered global model reduction schemes for PDEs.

Numerical bifurcation techniques for chemical reactor problems.- Path-following of large bifurcation problems with iterative methods.- On the bifurcation from continuous to segmented chip formation in metal cutting.- Using dynamical system tools in Matlab.- Formation and instabilities of coherent structures in channel flows.- Applications of smooth orthogonal factorizations of matrices.- Continuation of codimension-2 equilibrium bifurcations in Content.- Inclination-flips in the unfolding of a singular heteroclinic cycle.- Investigating torus bifurcations in the forced Van der Pol oscillator.- Quasiperiodic response to parametric excitations.- Self-organized criticality: analysis and simulation of a ID sandpile.- Computation and bifurcation analysis of periodic solutions of large-scale systems.- Multiple equilibria and stability of the north-atlantic wind-driven ocean circulation.- Numerical exploration of bifurcation phenomena associated with complex instability.- Chaos in traveling waves of lattice systems of unbounded media.- Pattern formation in a cellular slime mold.- Global parametrization and computation of resonance surfaces for periodically forced oscillators.- Computing invariant tori and circles in dynamical systems.- A Design problem for image processing.- Bifurcation analysis for timesteppers.- List of participants.