Simulation of the loss-cone instability in spherical systems. I.
  Dominating harmonic potential
  A new so-called `gravitational loss-cone instability' in stellar systems has
recently been investigated theoretically in the framework of linear
perturbation theory and proved to be potentially important in understanding the
physical processes in centres of galaxies, star clusters, and the Oort comet
cloud. Using N-body simulations of a toy model, we confirm previous findings
for the harmonic dominating potential and go beyond the linear theory. Unlike
the well-known instabilities, the new one shows no notable change in the
spherical geometry of the cluster, but it significantly accelerates the speed
of diffusion of particles in phase space leading to an early instability
saturation.
