  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. Typical applications are oscillator networks, but 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. A
second order Kuramoto model 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.
