Why do Chaotic Orbits Converge under a Random Velocity Reset?

When an ensemble of interacting identical particles is put inside a confining potential it is usually the case that the particle trajectories are chaotic and thus exhibit sensitive dependence on initial conditions. However, if their velocities are randomly reset at a regular time interval τ according to a prescribed probability distribution, then it might happen that all the particles will eventually converge to some unique yet irratic orbit in the physical space, depending on the pertinent physical parameters of the system and τ. We suggest that this is a rather general phenomenon, and give an argument in favor of this view. Scaling properties for the threshold reset time are also derived.