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A new so-called `gravitational loss-cone instability' in stellar systems hasrecently been investigated theoretically in the framework of linearperturbation theory and proved to be potentially important in understanding thephysical processes in centres of galaxies, star clusters, and the Oort cometcloud. Using N-body simulations of a toy model, we confirm previous findingsfor the harmonic dominating potential and go beyond the linear theory. Unlikethe well-known instabilities, the new one shows no notable change in thespherical geometry of the cluster, but it significantly accelerates the speedof diffusion of particles in phase space leading to an early instabilitysaturation.

Simulation of the loss-cone instability in spherical systems. I. Dominating harmonic potential