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Numerical detection of symmetry-breaking bifurcation points with nonlinear degeneracies

(1999) MATHEMATICS OF COMPUTATION. 68(227). p.1097-1108
Author
Organization
Abstract
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.
Keywords
symmetry-breaking bifurcation, EQUATIONS, nonlinear degeneracy, bordered, matrices, generalised Liapunov-Schmidt reduction, Newton-like method, pathfollowing

Citation

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Chicago
Bohmer, K, Willy Govaerts, and V Janovsky. 1999. “Numerical Detection of Symmetry-breaking Bifurcation Points with Nonlinear Degeneracies.” Mathematics of Computation 68 (227): 1097–1108.
APA
Bohmer, K., Govaerts, W., & Janovsky, V. (1999). Numerical detection of symmetry-breaking bifurcation points with nonlinear degeneracies. MATHEMATICS OF COMPUTATION, 68(227), 1097–1108.
Vancouver
1.
Bohmer K, Govaerts W, Janovsky V. Numerical detection of symmetry-breaking bifurcation points with nonlinear degeneracies. MATHEMATICS OF COMPUTATION. 1999;68(227):1097–108.
MLA
Bohmer, K, Willy Govaerts, and V Janovsky. “Numerical Detection of Symmetry-breaking Bifurcation Points with Nonlinear Degeneracies.” MATHEMATICS OF COMPUTATION 68.227 (1999): 1097–1108. Print.
@article{111450,
  abstract     = {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.},
  author       = {Bohmer, K and Govaerts, Willy and Janovsky, V},
  issn         = {0025-5718},
  journal      = {MATHEMATICS OF COMPUTATION},
  keyword      = {symmetry-breaking bifurcation,EQUATIONS,nonlinear degeneracy,bordered,matrices,generalised Liapunov-Schmidt reduction,Newton-like method,pathfollowing},
  language     = {eng},
  number       = {227},
  pages        = {1097--1108},
  title        = {Numerical detection of symmetry-breaking bifurcation points with nonlinear degeneracies},
  url          = {http://dx.doi.org/10.1090/S0025-5718-99-01052-2},
  volume       = {68},
  year         = {1999},
}

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