ABSTRACT
Prey-predator models, especially those with a neutral pattern of stability, are probably the most interesting target for investigating the stabilization effects of migration, which are the most likely to be certain in this case. Particular formulations of problems on the stabilization effects of migration are numerous. It is strongly believed, at least by theoretically minded ecologists, that the ability of a community to persist in spite of perturbations, is strongly promoted by its being distributed in space. Obviously, the linear relationship is by no means the only type of relationship by which the migration may depend on the population sizes of migrating species, but it is quite sufficient for the purpose of stability analysis as far as the analysis is to be done by the linearization method. For any pattern of biological interactions in an isolated subsystem, uniting by means of migration in an isotropic medium fails to improve the system stability properties.
