Results 241 to 250 of about 173,676 (290)

Double singularity-induced bifurcation points and singular Hopf bifurcations

Dynamics and Stability of Systems, 2000
The singularity-induced bifurcation and singular Hopf bifurcation theorems and the degeneracies that arise when Newton's laws are coupled to Kirchhoff's laws are explored. Such models are used in the electrical engineering literature to describe electrical power systems and they can take the form of either an index-1 differential-algebraic equation ...
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Computing multiple pitchfork bifurcation points

Computing, 1997
For the parameter dependent nonlinear equation \(F(x,\lambda) =0\), \(F: \mathbb{R}^n \times \mathbb{R}^1 \to\mathbb{R}^n\), the generically important case \(\text{rank} \partial_x E(x^*, \lambda^*) =n-1\) is investigated. In a neighborhood of such pitchfork bifurcation point \((x^*, \lambda^*)\) of multiplicity \(p\geq 1\) the Lyapunov-Schmidt ...
Pönisch, G., Schnabel, U., Schwetlick, H.   +2 more
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The Computation of Symmetry-Breaking Bifurcation Points

SIAM Journal on Numerical Analysis, 1984
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Werner, B., Spence, A.
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A numerical approach to hopf bifurcation points

Journal of Shanghai University (English Edition), 1998
Consider the \(n\)-dimensional autonomous system \({dx\over dt}= f(x,\alpha)\) depending on a real parameter \(\alpha\). The authors present a numerical method to detect a Hopf bifurcation point \(\alpha_0\) based on the computation of the largest Lyapunov exponent. The method is illustrated by means of two examples.
Yang, Zhonghua, Li, Changpin
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Bifurcation and Critical Point

2012
In Chap. 4, we use bifurcation and critical point theory together to study the structure of the solutions of elliptic equations; also we have results on three sign-changing solutions.
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Investigation of bifurcation points

1969
In sections 16 and 17 we encountered bifurcation points. In diagrams which represent the solutions depending on some parameter e, say, there exist special values of this parameter, es, where solutions coincide which for e ≠ es are of different character. Looked at e = es from another point of view we might say that at e = es a new solution branches off
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Undecidable hopf bifurcation with undecidable fixed point

International Journal of Theoretical Physics, 1994
Motivated by Hilbert's sixth problem and its contemporary revisions by V. I. Arnold [\textit{F. E. Browder}: ``Problems of present day mathematics'', Math. developments arising from Hilbert problems, Proc. Symp. Pure Math. 28, 35-79 (1976; Zbl 0326.00002), p.
da Costa, N. C. A., Doria, F. A.
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Anticipatory Systems near Bifurcation Points

AIP Conference Proceedings, 2006
Bifurcation in the sense of applied mathematics happens when the system is on the boundary of one set of equivalent states. Generally a system undergoing bifurcation is in a critical state. Any small change in the parameters may result essentially different behaviors.
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The homoclinic twist bifurcation point

1992
We analyze bifurcations occurring in the vicinity of a homoclinic twist point for a generic two parameter family of Z 2 equivariant ODE’s in four dimensions. The results are compared with numerical results for a system of two coupled Josephson junctions with pure capacitive load.
Aronson, D.G., van Gils, S.A., Krupa, M.
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Bifurcation Analysis of Nonlinear Turning Point Problems

SIAM Journal on Applied Mathematics, 1985
A bifurcation analysis is carried out on a class of nonlinear two-point boundary value problems for which the associated linearized equations have turning point structure. A perturbation method is used to study the behavior of solutions branching from large eigenvalues.
Lange, Charles G., Kriegsmann, Gregory A.   +1 more
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