Conditions for uniqueness of limit cycles in general predator-prey systems

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Abstract

Using a transformation to a generalized Lienard system, theorems are presented that give conditions under which unique limit cycles for generalized ecological systems, including those of predator-prey form, exist. The generalized systems contain those studied by Rosenzweig and MacArthur (1963); Hsu, Hubbell, and Waltman (1978); Kazarinnoff and van den Driessche (1978); Cheng (1981); Liou and Cheng (1987); and Kuang and Freedman (1988). Although very similar in approach to the result presented by Kuang and Freedman, the conditions presented here are of simpler form and in terms of the original (untransformed) functions. The results also apply to more general growth terms for the prey as shown in the examples provided. In particular, an immigration term is allowable. © 1989.

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Huang, X. C., & Merrill, S. J. (1989). Conditions for uniqueness of limit cycles in general predator-prey systems. Mathematical Biosciences, 96(1), 47–60. https://doi.org/10.1016/0025-5564(89)90082-5

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