Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Early-warning signals for bifurcations in random dynamical systems with
  bounded noise   We consider discrete-time one-dimensional random dynamical systems with
bounded noise, which generate an associated set-valued dynamical system. We
provide necessary and sufficient conditions for a discontinuous bifurcation of
a minimal invariant set of the set-valued dynamical system in terms of the
derivatives of the so-called extremal maps. We propose an algorithm for
reconstructing the derivatives of the extremal maps from a time series that is
generated by iterations of the original random dynamical system. We demonstrate
that the derivative reconstructed for different parameters can be used as an
early-warning signal to detect an upcoming bifurcation, and apply the algorithm
to the bifurcation analysis of the stochastic return map of the Koper model,
which is a three-dimensional multiple time scale ordinary differential equation
used as prototypical model for the formation of mixed-mode oscillation
patterns. We apply our algorithm to data generated by this map to detect an
upcoming transition.

3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin