Abstract
The scaling of the time delay near a ‘bottleneck’ of a generic saddle-node bifurcation is well known to be given by an inverse square-root law. We extend the analysis to several non-generic cases for smooth vector fields. We proceed to investigate C0 vector fields. Our main result is a new phenomenon in two-parameter families having a saddle-node bifurcation upon changing the first parameter. We find distinct scalings for different values of the second parameter ranging from power laws with exponents in (0, 1) to scalings given by O(1). We illustrate this rapid quantitative change of the scaling law by an overdamped pendulum with varying length.
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