Qualitative analysis of Kolmogorov-type models of predator-prey systems

The qualitative behaviors of Kolmogorov-type models are investigated under assumptions that are consistent with models of predator-prey systems and biologically realistic. The main purpose of this paper is to prove the boundedness of solutions and to give criteria for the existence of limit cycles for the system. In the case that the positive equilibrium is locally asymptotically stable, an example shows that there could be more limit cycles. This example serves as a counterexample to the global stability criterion of Huang.