This monograph is the first to provide readers with numerical tools for a systematic analysis of bifurcation problems in reaction-diffusion equations. Many examples and figures illustrate analysis of bifurcation scenario and implementation of numerical schemes. Readers will gain a thorough understanding of numerical bifurcation analysis and the necessary tools for investigating nonlinear phenomena in reaction-diffusion equations.

Inhalt

1. Reaction-Diffusion Equations.- 2. Continuation Methods.- 3. Detecting and Computing Bifurcation Points.- 4. Branch Switching at Simple Bifurcation Points.- 5. Bifurcation Problems with Symmetry.- 6. Liapunov-Schmidt Method.- 7. Center Manifold Theory.- 8. A Bifurcation Function for Homoclinic Orbits.- 9. One-Dimensional Reaction-Diffusion Equations.- 10. Reaction-Diffusion Equations on a Square.- 11. Normal Forms for Hopf Bifurcations.- 12. Steady/Steady State Mode Interactions.- 13. Hopf/Steady State Mode Interactions.- 14. Homotopy of Boundary Conditions.- 15. Bifurcations along a Homotopy of BCs.- 16. A Mode Interaction on a Homotopy of BCs.- List of Figures.- List of Tables.