On a predator-prey system of Gause type.
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.
Hasík
Karel
K
Institute of Mathematics, Silesian University, Na Rybnicku 1, 74601 Opava, Czech Republic. Karel.Hasik@math.slu.cz
D000818:Animals; D020387:Food Chain; D055641:Mathematical Concepts; D008954:Models, Biological; D011157:Population Dynamics; D011235:Predatory Behavior