Geometry of the Poincaré compactification of a four-dimensional food-web system

In this paper, the behavior of dynamics ‘at infinity’ of a four-dimensional autonomous food web system has been investigated. For this, a topological method has been developed to understand the geometry of the Poincaré compactification which investigate the behavior of the vector field at infinity. The global phase portrait has been shown on the Poincaré disc.