Anomalous scaling behavior in Takens-Bogdanov bifurcations

Physics – Classical Physics

Scientific paper

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6 pages

Scientific paper

10.1016/S0375-9601(98)00200-X

A general algorithm is presented for estimating the nonlinear instability threshold, $\sigma_c$, 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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