ABSTRACT
This 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.
Acknowledgments
The author would like to thank the anonymous referees for valuable suggestions which improved the paper.
Disclosure statement
No potential conflict of interest was reported by the author.