| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Humboldt Univ, Inst Phys, Berlin - Germany
[2] Humboldt Univ, Potsdam Inst Climate Impact Res, Inst Phys, Berlin - Germany
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | NEW JOURNAL OF PHYSICS; v. 22, n. 3 MAR 2020. |
| Web of Science Citations: | 0 |
| 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. (AU) | |
| FAPESP's process: | 15/50122-0 - Dynamic phenomena in complex networks: basics and applications |
| Grantee: | Elbert Einstein Nehrer Macau |
| Support Opportunities: | Research Projects - Thematic Grants |