Phase portraits of a family of Kolmogorov systems with infinitely many singular points at infinity

Abstract We give the topological classification of the global phase portraits in the Poincare disc of the Kolmogorov systems x = x a 0 + c 1 x + c 2 z 2 + c 3 z , z = z c 0 + c 1 x + c 2 z 2 + c 3 z , which depend on five parameters and have infinitely many singular points at the infinity. We prove that these systems have 22 topologically distinct phase portraits.