论文信息 - Numerical detection of symmetry breaking bifurcation points with nonlinear degeneracies

Numerical detection of symmetry breaking bifurcation points with nonlinear degeneracies

A numerical tool for the detection of degenerated symmetry breaking bifurcation points is presented. The degeneracies are classified and numerically processed on 1-D restrictions of the bifurcation equation. The test functions that characterise each of the equivalence classes are constructed by means of an equivariant numerical version of the Liapunov-Schmidt reduction. The classification supplies limited qualitative information concerning the imperfect bifurcation diagrams of the detected bifurcation points.

[1] W. Govaerts. Computation of Singularities in Large Nonlinear Systems , 1997 .

[2] Vladimír Janovský,et al. Numerical applications of equivariant reduction techniques , 1992 .

[3] M. Golubitsky,et al. Singularities and groups in bifurcation theory , 1985 .

[4] Karin Gatermann,et al. Automatic classification of normal forms , 1998 .

[5] A. Spence,et al. On a reduction process for nonlinear equations , 1989 .

[6] M. Dellnitz,et al. Computational methods for bifurcation problems with symmetries—with special attention to steady state and Hopf bifurcation points , 1989 .

[7] D. Roose,et al. Continuation Techniques and Bifurcation Problems , 1990 .