Continuation and Bifurcations: Numerical Techniques and Applications

Front Matter....Pages i-xiii
Bifurcation to Rotating Waves from Non-Trivial Steady-States....Pages 1-8
Use of Approximate Inertial Manifolds in Bifurcation Calculations....Pages 9-23
Understanding Steady-State Bifurcation Diagrams for a Model Reaction-Diffusion System....Pages 25-41
Bifurcations, Chaos and Self-Organization in Reaction-Diffusion Systems....Pages 43-70
Eigenvalue Problems with the Symmetry of a Group and Bifurcations....Pages 71-88
Steady-State/Steady-State Mode Interaction in Nonlinear Equations with Z 2 -Symmetry....Pages 89-103
Symbolic Computation and Bifurcation Methods....Pages 105-122
Bifurcation Analysis: A Combined Numerical and Analytical Approach....Pages 123-137
Introduction to the Numerical Solution of Symmetry- Breaking Bifurcation Problems....Pages 139-152
A Computational Method and Path Following for Periodic Solutions with Symmetry....Pages 153-167
Global Bifurcations and their Numerical Computation....Pages 169-181
Computation of Invariant Manifold Bifurcations....Pages 183-195
A Method for Homoclinic and Heteroclinic Continuation in Two and Three Dimensions....Pages 197-210
The Global Attractor Under Discretisation....Pages 211-225
The Numerical Detection of Hopf Bifurcation Points....Pages 227-246
A Newton-Like Method for Simple Bifurcation Problems with Application to Large Sparse Systems....Pages 247-259
Aspects of Continuation Software....Pages 261-268
Interactive System for Studies in Nonlinear Dynamics....Pages 269-282
LINLBF: A Program for Continuation and Bifurcation Analysis of Equilibria Up to Codimension Three....Pages 283-296
On the Topology of Three-Dimensional Separations, A Guide For Classification....Pages 297-318
The Construction of Cubature Formulae Using Continuation and Bifurcation Software....Pages 319-333
Determining an Organizing Center for Passive Optical Systems....Pages 335-345
Optimization by Continuation....Pages 349-362
Stability of Marangoni Convection in a MicroGravity Environment....Pages 363-377
Computing with Reaction-Diffusion Systems : Applications in Image Processing....Pages 379-387
Bifurcation of Codimension 2 for a discrete map....Pages 389-396
Bifurcation of periodic solutions in PDE’s: Numerical techniques and applications....Pages 397-399
Bifurcation and Chaos in Chua’s Circuit Family....Pages 401-403
Continuation and Collocation for Parameter Dependent Boundary Value Problems....Pages 405-405
Porous Medium Combustion....Pages 407-407
Block Elimination and the Computation of Simple Turning Points....Pages 409-409
Bifurcation Into Gaps in the Essential Spectrum....Pages 411-411
Application of Numerical Continuation in Aerospace Problems....Pages 413-413
Application of a Reduced Basis Method in Structural Analysis>....Pages 415-415
Some Applications of Bifurcation Theory in Engineering....Pages 417-417
Higher Order Predictors in Numerical Path Following Schemes....Pages 419-419
Back Matter....Pages 421-426