The authors discuss survival and extinction of predators in models of predator-prey systems exhibiting group defence of the prey. Such phenomena were less studied before. They show that if there is no mutual interference among predators, enrichment of the prey can lead to extinction in a closed ecosystem and thereby provide more support for Rosenzweig’s warning that is well-known and controverted.
But if there is mutual interference among predators, the model is uniformly persistent just as in previus work. Numerical examples are also indicated.
The models of this paper can be carefully studied with a specific response function. Recently, Zhang Faqin obtained conditions on existence and uniqueness of limit cycles and persistence and extinction for this model with generally chosen parameters (to appear in J. Biomath., Vol. 3).