Continuation and Bifurcations: Numerical Techniques and Applications

Abstract

Bifurcation to rotating waves from non-trivial steady-states.- Use of approximate inertial manifolds in bifurcation calculations.- Understanding steady-state bifurcation diagrams for a model reaction-diffusion system.- Bifurcations, chaos and self-organization in reaction-diffusion systems.- Eigenvalue problems with the symmetry of a group and bifurcations.- Steady-state/steady-state mode interaction in nonlinear equations with Z2-symmetry.- Symbolic computation and bifurcation methods.- Bifurcation analysis: a combined numerical and analytical approach.- to the numerical solution of symmetry-breaking bifurcation problems.- A computational method and path following for periodic solutions with symmetry.- Global bifurcations and their numerical computation.- Computation of invariant manifold bifurcations.- A method for homoclinic and heteroclinic continuation in two and three dimensions.- The global attractor under discretisation.- The numerical detection of Hopf bifurcation points.- A Newton-like method for simple bifurcation problems with application to large sparse systems.- Aspects of continuation software.- Interactive system for studies in nonlinear dynamics.- LINLBF: A program for continuation and bifurcation analysis of equilibria up to codimension three.- On the topology of three-dimensional separations, A guide for classification.- The construction of cubature formulae using continuation and bifurcation software.- Determining an Organizing Center for Passive Optical Systems.- Optimization by continuation.- Stability of Marangoni convection in a microgravity environment.- Computing with reaction-diffusion systems: applications in image processing.- Bifurcation of Codimension 2 for a discrete map.- Bifurcation of periodic solutions in PDE's: Numerical techniques and applications (abstract).- Bifurcation and chaos in Chua's circuit family (abstract).- Continuation and collocation for parameter dependent boundary value problems (abstract).- Porous medium combustion (abstract).- Block elimination and the computation of simple turning points (abstract).- Bifurcation into gaps in the essential spectrum (abstract).- Application of numerical continuation in aerospace problems (abstract).- Application of a reduced basis method in structural analysis (abstract).- Some applications of bifurcation theory in engineering (abstract).- Higher order predictors in numerical path following schemes (abstract).