Models of tolerant threshold behavior (from T. Shelling to M. Granovetter)

Models of tolerance are considered starting from the works of T. Shelling. It is shown, that tolerant threshold behavior, including the basic Shelling's model, could be equivalently transformed into the model of Granovetter with certain cumulative distribution function of thresholds. The model describing agents' competition inside a group with their sympathies outside of this group (a sort of “upside-down tolerance”) is studied. These both types of behavior are explored in continuous time, additionally considering the effects of forgetting and delay leading to damped and undamped oscillations.