Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tipping points near a delayed saddle node bifurcation with periodic
  forcing   We consider the effect on tipping from an additive periodic forcing in a
canonical model with a saddle node bifurcation and a slowly varying bifurcation
parameter. Here tipping refers to the dramatic change in dynamical behavior
characterized by a rapid transition away from a previously attracting state. In
the absence of the periodic forcing, it is well-known that a slowly varying
bifurcation parameter produces a delay in this transition, beyond the
bifurcation point for the static case. Using a multiple scales analysis, we
consider the effect of amplitude and frequency of the periodic forcing relative
to the drifting rate of the slowly varying bifurcation parameter.
  We show that a high frequency oscillation drives an earlier tipping when the
bifurcation parameter varies more slowly, with the advance of the tipping point
proportional to the square of the ratio of amplitude to frequency. In the low
frequency case the position of the tipping point is affected by the frequency,
amplitude and phase of the oscillation. The results are based on an analysis of
the local concavity of the trajectory, used for low frequencies both of the
same order as the drifting rate of the bifurcation parameter and for low
frequencies larger than the drifting rate. The tipping point location is
advanced with increased amplitude of the periodic forcing, with critical
amplitudes where there are jumps in the location, yielding significant advances
in the tipping point. We demonstrate the analysis for two applications with
saddle node-type bifurcations.

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The categories of this paper are: stat
12
The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
3
The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th