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Anomalous scaling behavior in Takens-Bogdanov bifurcations

E. R. Tracy·X. Z. Tang
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Abstract

A general algorithm is presented for estimating the nonlinear instability threshold, $σ_c$, for subcritical transitions in systems where the linearized dynamics is significantly non-normal (i.e. subcritical bifurcations of {\em Takens-Bogdanov} type). The $N$-dimensional degenerate node is presented as an example. The predictions are then compared to numerical studies with excellent agreement.

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E. R. Tracy, X. Z. Tang. 1998-02-27. Anomalous scaling behavior in Takens-Bogdanov bifurcations. https://doi.org/10.1016/s0375-9601(98)00200-x

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