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  Monte Carlo basin bifurcation analysis

Gelbrecht, M., Kurths, J., Hellmann, F. (2020): Monte Carlo basin bifurcation analysis. - New Journal of Physics, 22, 033032.
https://doi.org/10.1088/1367-2630/ab7a05

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 Creators:
Gelbrecht, Maximilian1, Author              
Kurths, Jürgen1, Author              
Hellmann, Frank1, Author              
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1Potsdam Institute for Climate Impact Research, ou_persistent13              

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 Abstract: Many high-dimensional complex systems exhibit an enormously complex landscape of possible asymptotic states. Here, we present a numerical approach geared towards analyzing such systems. It is situated between the classical analysis with macroscopic order parameters and a more thorough, detailed bifurcation analysis. With our machine learning method, based on random sampling and clustering methods, we are able to characterize the different asymptotic states or classes thereof and even their basins of attraction. In order to do this, suitable, easy to compute, statistics of trajectories with randomly generated initial conditions and parameters are clustered by an algorithm such as DBSCAN. Due to its modular and flexible nature, our method has a wide range of possible applications in many disciplines. While typical applications are oscillator networks, it is not limited only to ordinary differential equation systems, every complex system yielding trajectories, such as maps or agent-based models, can be analyzed, as we show by applying it the Dodds–Watts model, a generalized SIRS-model, modeling social and biological contagion. A second order Kuramoto model, used, e.g. to investigate power grid dynamics, and a Stuart–Landau oscillator network, each exhibiting a complex multistable regime, are shown as well. The method is available to use as a package for the Julia language.

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 Dates: 2020
 Publication Status: Finally published
 Pages: -
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 Rev. Type: Peer
 Identifiers: DOI: 10.1088/1367-2630/ab7a05
PIKDOMAIN: RD4 - Complexity Science
eDoc: 8990
MDB-ID: pending
Research topic keyword: Complex Networks
Research topic keyword: Nonlinear Dynamics
Model / method: Machine Learning
Organisational keyword: RD4 - Complexity Science
Working Group: Development of advanced time series analysis techniques
Working Group: Network- and machine-learning-based prediction of extreme events
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Title: New Journal of Physics
Source Genre: Journal, SCI, Scopus, p3, oa
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Pages: - Volume / Issue: 22 Sequence Number: 033032 Start / End Page: - Identifier: CoNE: https://publications.pik-potsdam.de/cone/journals/resource/1911272
Publisher: IOP Publishing