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Interactions leading to persistence in predator-prey systems with group defence. (English) Zbl 0673.92011

This paper deals with the study of a predator-prey system where the prey exhibits group defence, and there is a third interacting population. The model is a system of autonomous Kolmogorov-type differential equations, with several hypotheses that take into account previous work by the first author and G. S. Wolkowicz, ibid. 48, 493-508 (1986; Zbl 0612.92017), on predator-prey systems with group defence.

The study of the system to obtain criteria for persistence of all populations is done through the study of periodic orbits. Conditions for persistence are obtained and two special cases are presented. The biological interpretation of the conditions is given for some of them, the other having, for the moment, a purely mathematical sense.

Reviewer: H.de Arazoza
MSC:
92D40Ecology
92D25Population dynamics (general)