A paradoxical instability caused by relatively short-range inhibition

Many dynamical systems, with dependence on spatial or analogous “aspect” Variables, possess a uniform state that can exhibit instabilities in the presence of short-range activation and long-range inhibition. It has recently been shown that a model of the immune system can give rise to instabilities in the opposite case, when inhibition is relatively short range. An explanation for this surprising result is offered here, together with some numerical calculations that show the development of the instability in time.