Abstract
In this paper a Gause type model of interactions between predator and prey population is considered. We deal with the sufficient condition due to Kuang and Freedman in the generalized form including a kind of weight function. In a previous paper we proved that the existence of such weight function implies the uniqueness of limit cycle. In the present paper we give a new condition equivalent to the existence of a weight function (Theorem 4.4). As a consequence of our result, it is shown that some simple qualitative properties of the trophic function and the prey isocline ensure the uniqueness of limit cycle.
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The research of this author was supported, in part, by projects 201/06/0318 from the Czech Science Foundation, and MSM4781305904 from the Czech Ministry of Education. Support of these institutions is gratefully acknowledged.
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Hasík, K. On a predator–prey system of Gause type. J. Math. Biol. 60, 59–74 (2010). https://doi.org/10.1007/s00285-009-0257-8
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DOI: https://doi.org/10.1007/s00285-009-0257-8