The Computation of Symmetry-Breaking Bifurcation Points
- 1 April 1984
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Numerical Analysis
- Vol. 21 (2), 388-399
- https://doi.org/10.1137/0721029
Abstract
We consider symmetry-breaking simple singular points of a parameter dependent nonlinear equation $g(\lambda ,x) = 0$. Such points are intimately connected to pitchfork bifurcation points, and we show that they can be computed in a stable way using a suitable extended system. Because of the underlying symmetry this system is much simpler than other extended systems for the computation of secondary bifurcation points.
Keywords
This publication has 19 references indexed in Scilit:
- Numerical calculations of two-cell and single-cell Taylor flowsJournal of Fluid Mechanics, 1983
- A comparison of methods for determining turning points of nonlinear equationsComputing, 1982
- Finite dimensional approximation of nonlinear problemsNumerische Mathematik, 1982
- Numerical analysis of continuation methods for nonlinear structural problemsComputers & Structures, 1981
- The Calculation of Turning Points of Nonlinear EquationsSIAM Journal on Numerical Analysis, 1980
- The numerical treatment of non-trivial bifurcation pointsNumerical Functional Analysis and Optimization, 1980
- Imperfect bifurcation in the presence of symmetryCommunications in Mathematical Physics, 1979
- A theory for imperfect bifurcation via singularity theoryCommunications on Pure and Applied Mathematics, 1979
- An efficient algorithm for the determination of certain bifurcation pointsJournal of Computational and Applied Mathematics, 1978
- Multiple Eigenvalues Lead to Secondary BifurcationSIAM Review, 1975