We rep o rt here a h o st-m acro p arasite interaction in which several types of attractors m ay coexist. A proportion of host p o p ulation is im m une to the parasite. T he basic attractors observed in this two-species interaction include p o int equilibria, 2-, 3-, 6-, 12-, and 8-cycles, quasicycles, and 3-piece and 6-piece chaotic attractors. T h e attracto rs depend on the initial population levels as well as on the proportion of im m une hosts. C hanges in the proportion of im m une hosts

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... m ay either stabilize or destabilize the interaction. T h e non-uniqueness of the attractors implies th at the bifurcation diagram s, or the routes to chaos, m ay also not be unique, b u t m ay depend on the specific initial population level chosen. T he basins of attractio n , defining the initial conditions leading to a certain type of an attracto r, m ay be fractal sets, even in the case of two non-chaodc attractors. T he fractal property observed is the p attern of self sim ilarity. It follows th a t sensitivity of the trajectory with respect to the initial condition can be observed in the absence of chaos in the dynam ics.