Abstract
Perturbation methods are applied to a differential equation predator-prey model to find the approximate amplitudes and period of limit cycle solutions. In the model the feeding rate per unit predator per unit prey decreases as the prey become scare. The rigorous applicability of the perturbation technique depends on the assumptions that the limit cycle amplitude is relatively small and that near the equilibrium point the growth rate of each species is most sensitive to changes in the density of the other species. The second assumption is usually roughly satisfied in practice and examples are considered which suggest that the first assumption can be greatly relaxed.
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De Angelis, D.L. Estimates of predator-prey limit cycles. Bltn Mathcal Biology 37, 291–299 (1975). https://doi.org/10.1007/BF02461447
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DOI: https://doi.org/10.1007/BF02461447