FORCED ASYMPTOTICALLY PERIODIC SOLUTIONS OF PREDATOR-PREY SYSTEMS WITH OR WITHOUT HEREDITARY EFFECTS.

V. Volterra's two-species predator-prey integro-differential model, which describes the dynamics of predator-prey interactions when continuously accumulating lag effects are considered, is modified by the addition of forcing or control functions. It is shown that for appropriate choices of these control functions the model possesses infinitely many asymptotically periodic solutions for small logistic loads and hereditary (or lag) effects. For certain special cases the existence of periodic solutions is proved.