  For certain dynamical systems it is possible to significantly simplify the
study of stability by means of the center manifold theory. This theory allows
to isolate the complicated asymptotic behavior of the system close to a
non-hyperbolic equilibrium point, and to obtain meaningful predictions of its
behavior by analyzing a reduced dimensional problem. Since the manifold is
usually not known, approximation methods are of great interest to obtain
qualitative estimates. In this work, we use a data-based greedy kernel method
to construct a suitable approximation of the manifold close to the equilibrium.
The data are collected by repeated numerical simulation of the full system by
means of a high-accuracy solver, which generates sets of discrete trajectories
that are then used to construct a surrogate model of the manifold. The method
is tested on different examples which show promising performance and good
accuracy.
