The Institute for Mathematics and its Applications (IMA) devoted its 1 997-1998 program to Emerging Applications of Dynamical Systems. Dynami cal systems theory and related numerical algorithms provide powerful t ools for studying the solution behavior of differential equations and mappings. In the past 25 years computational methods have been develop ed for calculating fixed points, limit cycles, and bifurcation points. A remaining challenge is to develop robust methods for calculating mo re complicated objects, such as higher-codimension bifurcations of fix ed points, periodic orbits, and connecting orbits, as well as the calc uation of invariant manifolds. Another challenge is to extend the appl icability of algorithms to the very large systems that result from dis cretizing partial differential equations. Even the calculation of stea dy states and their linear stability can be prohibitively expensive fo r large systems (e.g. 10_3-10_6 equations) if attempted by simple dire ct methods.
|Publisher:||Springer New York|
|Series:||The IMA Volumes in Mathematics and its Applications , #119|
|Edition description:||Softcover reprint of the original 1st ed. 2000|
|Product dimensions:||6.10(w) x 9.25(h) x 0.04(d)|
Table of ContentsNumerical 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.