DIE UNTERSUCHUNG DER DYNAMIK DER ZIP-BIFURKATION

Abstract

Two population dynamical models are studied where two predators are competing fer a single regenerating prey species. These models are three dimensional systems of differential equations, and the sta- bility of their equilibria and bifurcations with the increase of the carrying capacity (K) are studied. It is proved that under special assumptions all ratios of the predators are stable. In the special case of the Ivlevmodel there is not a significant difference in the response of the two predators, at a K-limit all the ratios of predators are simultaneously becoming unstable with a supercritical Hopf bifurcation. In the typical case we can see the competition of a K- and an r-strategist. The 1055 of stability happens by Zip bifurcation. In the Rosenzweigmodel competition between K- and r-strategist cannot take place.