Results 251 to 260 of about 173,676 (290)

Numerical Computation of Degenerate Hopf Bifurcation Points

ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik, 1998
In this paper a numerical method for the detection and computation of degenerate Hopf bifurcation points is presented. the degeneracies are classified and defining equations characterizing each of the equivalence classes are constructed by means of a generalized Liapunov-Schmidt reduction.
Xu, H., Janovský, V., Werner, B.
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NON CRITICAL BIFURCATION POINTS

1987
Trieste
AUGENTI, NICOLA, RAITHEL A., DELLA SALA L.   +2 more
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Computing bifurcation points via characteristics gain loci

IEEE Transactions on Automatic Control, 1991
Summary: This note shows how to check the crossing on the imaginary axis by the eigenvalues of the linearized system of differential equations depending on a real parameter \(\mu\) via feedback system theory. We present simple formulas for both, static (one eigenvalue zero) and dynamic or Hopf (a single pure imaginary pair) bifurcations.
Moiola, Jorge, Desages, Alfredo, Romagnoli, José   +2 more
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Direction of branches bifurcating at a bifurcation point. determination of starting points for a continuation algorithm

Applied Mathematics and Computation, 1983
Dans cet article les AA. considèrent des systèmes de n équations algébriques non linéaires \(f_ i(x_ 1,x_ 2,...,x_ n,\alpha)=0\), \(i=1,2,...,n\), dépendant du paramètre \(\alpha\). Des points de bifurcation, qui sont des points d'intersection de deux ou plusieurs branches de solutions, peuvent se présenter. Les AA.
Kubiček, Milan, Klič, Alois
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Lie-point symmetries in bifurcation problems

1992
The authors develop a theory of bifurcations of differential equations with Lie point symmetries. Viewing the differential equation as an ``algebraic equation'' on some jet bundle is the key of the analysis. The authors show how the well-known results of equivariant bifurcation theory can be formulated in this context and how the results carry over ...
CICOGNA, GIAMPAOLO, Gaeta G.
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Detecting and Computing Bifurcation Points

2000
Exploring nonlinear phenomena has become a major challenge in physics, chemistry, biology, engineering, medicine and social science. We consider nonlinear problems of the form $$\frac{{\partial u}}{{\partial t}} = G(u,\lambda ) $$ (3.1) where G : X x R p → Y is a “smooth” mapping and λ ∈ R p represents various control parameters, e.g ...
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Continuation of Newton’s Method Through Bifurcation Points

Journal of Applied Mechanics, 1969
A modification of Newton’s method is suggested that provides a practical means of continuing solutions of nonlinear differential equations through limit points or bifurcation points. The method is applicable when the linear “variational” equations for the problem are self-adjoint.
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FOLLOWING PATHS OF SYMMETRY-BREAKING BIFURCATION POINTS

International Journal of Bifurcation and Chaos, 1992
We propose a pseudo-arclength continuation algorithm for computing paths of Z 2-symmetry-breaking bifurcation points for two-parameter nonlinear elliptic problems. The algorithm consists of an Euler predictor step and a solution step composed of a sequence of Newton iterations.
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A note on Computing simple bifurcation points

Computing, 1989
The author suggests a modification for the implementation of a method which is originally due to \textit{G. Pönisch} [Computing 35, 277-294 (1985; Zbl 0569.65041)]. There is a numerical example.
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Counting Central Configurations at the Bifurcation Points

Acta Applicandae Mathematicae, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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