Global structure of subharmonics in a class of periodic predator-prey models

Abstract

This paper ascertains the global topological structure of the set of subharmonics of arbitrary order of the periodic predator-prey model introduced in López-Gómez et al (1996 Adv. Differ. Equ. 1 403–23). By constructing the iterates of the monodromy operator of the system, it is shown that the system admits subharmonics of all orders for the appropriate ranges of values of the parameters. Then, some sharp results of topological nature in the context of global bifurcation theory provide us with the fine topological structure of the components of subharmonics emanating from the T-periodic coexistence state.