On the global behaviour of May's host–parasitoid model

Abstract

ABSTRACTThis article investigates the global behaviour of May's host–parasitoid model [R.M. May, Host–parasitoid systems in patchy environments: A phenomenological model, J. Anim. Ecol. 47 (1978), pp. 833–844]. When and k>1, it is shown that solutions which have initial conditions in the complement of a bounded subset of the positive quadrant are unbounded. Further, it is shown that for these initial conditions, both the host and parasitoid populations oscillate with infinitely increasing amplitude.