Phase portraits of predator--prey systems with harvesting rates (Q765081)

The authors consider positive equilibria and phase portraits of predator-prey systems with constant harvesting rates arising in ecology. These systems are generalizations of the well-known predator-prey systems with Beddington-DeAngelis functional responses. The authors prove that these positive equilibria are saddles, topological saddles, nodes, saddle-nodes, foci, centers, or cusps by providing suitable ranges of the five parameters. These results show how the harvesting rate and another parameter used in Beddington-DeAngelis functional responses affect the dynamical behavior of these systems. In particular, if the harvesting rate is larger than \(1/4\) or the parameter just mentioned is too large, then mutual extinction occurs.