Titlebook: Numerical Methods for Bifurcation Problems; Proceedings of the C T. Küpper,H. D. Mittelmann,H. Weber Conference proceedings 1984 Springer B

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monopoly

slipped-disk

Techniques for Large Sparae Systems Arising from Continuation Methods,f parameterized nonlinear systems of the form G(u,λ) = 0. We concentrate on large and sparse problems, e.g. discretizations of partial differential equations, for which this part of the computation dominates the overall cost. The basic issue is a tradeoff of the exploitation of the sparsity structur

MELON

The Calculation of High Order Singularities in the Finite Taylor Problem,with small aspect ratio. A recent theoretical and experimental study was carried out by Benjamin and Mullin [1] and numerical results, which are in good agreement with those in [1], are given by Cliffe [3]. These results are summarized in figure 2.1 which gives the projection of paths of singular po

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是他笨

,Continuation of Periodic Solutions in Ordinary Differential Equations — Numerical Algorithm and App is based on the shooting method coupled with continuation along the arc of the Solution locus. The stability of periodic solutions is determined by characteristic multipliers computed in the course of the continuation.

事與愿違

Singular Points and their Computation,. ∈ .. is the state variable, λ ∈ . is the bifurcation parameter, and α ∈ .. is a vector of control parameters. The distinction of the bifurcation parameter λ from the control parameters α is made for two reasons. Firstly, it is often the case in experirnents that one parameter is varied quasi-stati

易彎曲

On a General Technique for Finding Directions Proceeding from Bifurcation Points,own á priori. The author previously introduced a method applicable when such information is not present, or when the arcs intersect tangentially. That method is discussed here, with particular emphasis on avenues to improvement in efficiency and reliability.

大洪水

,Numerical Deterkination of Bifurcation Points in Steady State and Periodic Solutions — Numerical Alit points in a distributed parameter system where shooting method cannot be used are shown in the form of bifurcation diagram. Four direct iteration algorithms for an evaluation of complex (Hopf) bifurcation points in lumped parameter systems (ordinary differential equations) are described and appli

Myelin

Feedback Stimulated Bifurcation*,er it is often easy to determine the bifurcation points experimentally since they are characterized by a significant change in the Output. For example think of the change from a constant to a periodic motion which is really evident since it appears as a qualitative rather than a quantitative change.