"Spatial self-organization in interacting particle systems with cyclic local dynamics"
We consider a class of stochastic spatial models characterized by local dynamics that have individual sites changing state in a strict cyclic progression. These include generalizations of epidemic models, rock-scissors-paper type competition models, host-parasitoid, etc. In some of these models, spatio-temporal self-organization is required for persistence of the system. We compare the behavior of the PDE's and Interacting Particle Systems. Throughout, we emphasize issues of persistence and pattern formation. Our individual-based model is both stochastic and spatially explicit.