Abstract

In this paper by using the Poincaré compactification of ℝ3 we make a global analysis of the model xʹ = ax + y + yz, yʹ = x–ay + bxz, zʹ = cz–bxy. In particular we give the complete description of its dynamics on the infinity sphere. For a + c = 0 or b = 1 this system has invariants. For these values of the parameters we provide the global phase portrait of the system in the Poincaré ball. We also describe the α and ω-limit sets of its orbits in the Poincaré ball.