Early-warning signals for bifurcations in random dynamical systems with bounded noise

@article{Kuehn2018EarlywarningSF,
  title={Early-warning signals for bifurcations in random dynamical systems with bounded noise},
  author={Christian Kuehn and Giuseppe Malavolta and Martin Rasmussen},
  journal={Journal of Mathematical Analysis and Applications},
  year={2018}
}
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… 
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