The stability of population oscillations in ecological systems is considered. Experiments suggest that in many cases the single patch dynamics of predator prey or host-parasite systems is extinction prone and stability is achieved only when the spatial structure of the population is expressed via desynchronization between patches. A few mechanisms have been suggested so far to explain the inability of dispersal to synchronize the system. We suggest a classification scheme that allows for either a-priori (based on the system parameters) or a posteriori (based on local measurements) identification of the dominant process that yields desynchronization.