Limit cycles in a generalized Gause-type predator-prey system

The qualitative behavior of solutions for a generalized Gause-type predator-prey system was studied. A large number of biological and bioeconomic models are special cases: of this system. The system was investigated in the region D = ( (x, y) \ x > 0, y > 0) because of the biological meaning of the system. The authors derived some sufficient conditions for the boundedness of the solutions and the existence of limit cycles of the system,which ensure that the system has at least one limit cycle. The theory of limit sets of autonomous plane systems and the theorem of cycle field of Poincare-Bendixson are efficiently employed in the research. The main results and their consequences presented not only generalize some known results, but also improve some corresponding results of other authors.