- The time evolution of a computer model for an isolated disk representing a flat galaxy is studied. The method of direct integration of Newton’s equations of motion of particles-"stars" is applied. Using the modern 128-processor SGI Origin 2000 supercomputer in Israel, we make long simulation runs with a large number of particles, N = 100 000. One of the goals of the simulation is to test the validities of the modified Safronov-Toomre criterion for stability of arbitrary but not only axisymmetric Jeans-type gravity disturbances (e.g., those produced by a spontaneous perturbation and/or a companion system) in a self-gravitating, thin, and almost collisionless stellar disk. We are also interested in how model particles diffuse in chaotic (residual) velocity space. This is of considerable interest in the nonlinear theory of stellar disks.