Journal of the
Korean Mathematical Society JKMS

We propose a cubic differential system, which can be considered a generalization of the predator-prey models, studied by many authors recently (see [18, 20], for instance). The properties of the equilibrium points, the existences, nonexistence, the uniqueness conditions and the relative positions of the limit cycles are investigated. An example is used to show our theorems are easy to be used in applications.

Keywords: cubic system, predator-prey, limit cycles, relative position

MSC numbers: 34A34, 92D25