Journal ArticleDOI
Secondary Bifurcation and Multiple Eigenvalues
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Secondary bifurcation of general nonlinear operator equations is studied in the neighborhood of multiple eigenvalues of the linearized problem in this paper, where necessary and sufficient conditions for the existence of such points are derived.Abstract:
Secondary bifurcation of general nonlinear operator equations is studied in the neighborhood of multiple eigenvalues of the linearized problem. Necessary conditions for the existence of secondary bifurcation are derived and the location of points of secondary bifurcation are found. The geometrical significance of these conditions is discussed and conditions on primary bifurcation at a multiple eigenvalue are found which guarantee the existence of points of secondary bifurcation.read more
Citations
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Hopf bifurcation and symmetry: travelling and standing waves on the circle
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Imperfection sensitivity of hilltop branching points of systems with dihedral group symmetry
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References
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Journal ArticleDOI
Some global results for nonlinear eigenvalue problems
TL;DR: In this paper, the structure of the solution set for a large class of nonlinear eigenvalue problems in a Banach space is investigated, and the existence of continua, i.e., closed connected sets, of solutions of these equations is demonstrated.
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A Theory for Imperfect Bifurcation via Singularity Theory.
TL;DR: In this paper, the authors apply the theory of singularities of differentiable mappings (SOMD) to study the effect of imperfections in a system subject to bifurcation.
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Multiple Eigenvalues Lead to Secondary Bifurcation
TL;DR: In this article, it is shown that a multiple bifurcation point may split into two (or more) simple primary points and several secondary points as the primary points vary from one point to another.
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Branching of Solutions of Nonlinear Equations
TL;DR: In this paper, a branch point is defined as a non-linear operator from a nonlinear operator into a Banach space such that the branch point tends to zero as tends to some particular value, a so-called branch point.