Preprint MA 63/2007

On a predator-prey system of Gause type

Karel Hasík

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. We give a necessary and sufficient condition under which this weight function exists. Moreover, 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.