JOURNAL ARTICLE
Numerical computation of symmetry-breaking bifurcation points
Year: 1993 Journal: The Journal of the Australian Mathematical Society Series B Applied Mathematics Vol: 35 (1)Pages: 103-113 Publisher: Cambridge University Press
Abstract
Abstract We consider symmetry-breaking bifurcation points which arise in parameter-dependent nonlinear equations of the form f ( x , λ) = 0. These types of bifurcation points are connected to pitchfork bifurcation points. A direct method is used to compute such points. Multiple shooting is used to discretise the two-point boundary-value problems to obtain a finite-dimensional problem.
Keywords:
Pitchfork bifurcation Bifurcation Transcritical bifurcation Bifurcation theory Mathematics Symmetry breaking Saddle-node bifurcation Infinite-period bifurcation Symmetry (geometry) Computation Bifurcation diagram Mathematical analysis Shooting method Nonlinear system Boundary (topology) Boundary value problem Bogdanov–Takens bifurcation Geometry Physics Algorithm Quantum mechanics
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5
Cited By
0.89
FWCI (Field Weighted Citation Impact)
12
Refs
0.76
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Citation History
Topics
Numerical methods for differential equations
Physical Sciences → Mathematics → Numerical Analysis
Matrix Theory and Algorithms
Physical Sciences → Computer Science → Computational Theory and Mathematics
Numerical methods in inverse problems
Physical Sciences → Mathematics → Mathematical Physics
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