Limit cycles in a general Kolmogorov model

The problem of limit cycles is interesting and significant both in theory and applications. In mathematical ecology, finding models that display a stable limit cycle-an attracting stable self-sustained oscillation, is a primary work. In this paper, a general Kolmogorov system, which includes the Gause-type model (Math. Biosci. 88 (1988) 67) the general predator-prey model (J. Phys. A: Math. Gen. 21 (1988) L685; Math. Biosci. 96 (1989) 47), and many other models (J. Biomath. 15(3) (2001) 266; J. Biomath. 16(2) (2001) 156; J. Math. 21(22) (2001) 145), is studied. The conditions for the existence and uniqueness of limit cycles in this model are proved. Some known results are easily derived as an illustration of our work. (C) 2004 Elsevier Ltd. All rights reserved.