Geometric criteria for the nonexistence of cycles in Gause-type predator-prey systems

Liu, Yaping

doi:10.1090/S0002-9939-05-08026-3

Geometric criteria for the nonexistence of cycles in Gause-type predator-prey systems
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by Yaping Liu

Proc. Amer. Math. Soc. 133 (2005), 3619-3626

DOI: https://doi.org/10.1090/S0002-9939-05-08026-3

Published electronically: June 8, 2005

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Abstract:

The global stability of a multi-species interacting system has apparently important biological implications. In this paper we study the global stability of Gause-type predator-prey models by providing new criteria for the nonexistence of cycles and limit cycles. Our criteria have clear geometrical interpretations and are easier to apply than other methods employed in recent studies. Using these criteria and related techniques we are able to develop new results on the existence and uniqueness of cycles in Gause-type models with various growth and response functions.

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