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This paper ascertains the global topological structure of the set ofsubharmonics of arbitrary order of the periodic predator-prey model introducedin L\'opez-G\'omez, Ortega and Tineo in 1996. By constructing the iterates ofthe monodromy operator of the system, it is shown that the system admitssubharmonics of all orders for the appropriate ranges of values of theparameters. Then, some sharp results of topological nature in the context ofglobal bifurcation theory provide us with the fine topological structure of thecomponents of subharmonics emanating from the T-periodic coexistence state.

Multiplicity of subharmonics in a class of periodic predator-prey Volterra models