  The stabilizing effects of local enrichment are revisited. Diffusively
coupled host-parasitoid and predator-prey metapopulations are shown to admit a
stable fixed point, limit cycle or stable torus with a rich bifurcation
structure. A linear toy model that yields many of the basic qualitative
features of this system is presented. The further nonlinear complications are
analyzed in the framework of the marginally stable Lotka-Volterra model, and
the continuous time analog of the unstable, host-parasitoid Nicholson-Bailey
model. The dependence of the results on the migration rate and level of spatial
variations is examined, and the possibility of "nonlocal" effect of enrichment,
where local enrichment induces stable oscillations at a distance, is studied. A
simple method for basic estimation of the relative importance of this effect in
experimental systems is presented and exemplified.
