Chapter 4 – Numerical Continuation, and Computation of Normal Forms

By W. Beyn, A. Champneys, Eusebius J. Doedel, Willy Govaerts, Y. Kuznetsov, Bjorn Sandstede. 2002

137 citations recorded by the source corpus.

Subfields: Numerical Analysis, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/09f52abb09d783865c4ef2cf5af6454802bd2b93

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Citations in the corpus

• The entwined wiggling of homoclinic curves emerging from saddle-node/Hopf instabilities (2004, background): “Such a philosophy was developed by Beyn [2] for starting homoclinic curves in the simpler case of a Takens{Bogdanov bifurcation (see also [ 3 ]).”
• A Survey of Methods for Computing (un)Stable Manifolds of Vector Fields (2005, unknown): “Most existing continuation algorithms can handle the computation of such one-dimensional families (also called solution branches); see, for example, [Beyn et al., 2002, Doedel et al., 1991a, Doedel et al., 1991b, Keller, 1977, Rheinboldt, 1986, Seydel, 1995], and [Kuznetsov, 1998, Chapter 10].”
• Continuation and Bifurcation Analysis of Delay Differential Equations (2007, background): “This can be achieved by using the bordering theorem [ 9 ], which states that the bordered operator”