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@article{Kuehn:2018:10.1016/j.jmaa.2018.03.066,
author = {Kuehn, C and Malavolta, G and Rasmussen, M},
doi = {10.1016/j.jmaa.2018.03.066},
journal = {Journal of Mathematical Analysis and Applications},
pages = {58--77},
title = {Early-warning signals for bifurcations in random dynamical systems with bounded noise},
url = {http://dx.doi.org/10.1016/j.jmaa.2018.03.066},
volume = {464},
year = {2018}
}

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TY  - JOUR
AB  - We consider discrete-time one-dimensional random dynamical systems withbounded noise, which generate an associated set-valued dynamical system. Weprovide necessary and sufficient conditions for a discontinuous bifurcation ofa minimal invariant set of the set-valued dynamical system in terms of thederivatives of the so-called extremal maps. We propose an algorithm forreconstructing the derivatives of the extremal maps from a time series that isgenerated by iterations of the original random dynamical system. We demonstratethat the derivative reconstructed for different parameters can be used as anearly-warning signal to detect an upcoming bifurcation, and apply the algorithmto the bifurcation analysis of the stochastic return map of the Koper model,which is a three-dimensional multiple time scale ordinary differential equationused as prototypical model for the formation of mixed-mode oscillationpatterns. We apply our algorithm to data generated by this map to detect anupcoming transition.
AU  - Kuehn,C
AU  - Malavolta,G
AU  - Rasmussen,M
DO  - 10.1016/j.jmaa.2018.03.066
EP  - 77
PY  - 2018///
SN  - 0022-247X
SP  - 58
TI  - Early-warning signals for bifurcations in random dynamical systems with bounded noise
T2  - Journal of Mathematical Analysis and Applications
UR  - http://dx.doi.org/10.1016/j.jmaa.2018.03.066
UR  - http://arxiv.org/abs/1803.00382v1
UR  - http://hdl.handle.net/10044/1/58434
VL  - 464
ER  -

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