On the applicability of the Poincaré-Birkhoff twist theorem to a class of planar periodic predator-prey models
The authors deal with the existence of subharmonics of arbitrary order in a generalized class of non-autonomous predator-prey systems of Volterra type with periodic coefficients. When the model is non-degenerate it is shown that the Poincaré-Birkhoff twist theorem can be applied to get the existence of subharmonics of arbitrary order. However, in the degenerate models, whether or not the twist theorem can be applied to get subharmonics of a given order might depend on the particular nodal behavior of the several weight function coefficients involved in the setting of the model. Finally, in order to analyze how the subharmonics might be lost as the model degenerates, the exact point-wise behavior of the T-periodic solutions of a non-degenerate model is ascertained as a perturbation parameter makes it degenerate. This is a valuable work in this field.
periodic predator-prey model of Volterra type
point-wise behavior of the low order subharmonics as the model degenerates
scientific article; zbMATH DE number 7190113