Phase portrait of a differential equations system modeling competitive interaction

The 6-parametric family of 3-dimentional autonomous ordinary differential equations systems is considered. Systems of that type are classic in the dynamic modeling of competitive interaction in populations, when there are three interacting groups. Such systems can be used in other spheres where we model the dynamics of competitive processes for three groups. We consider the systems on the invariant triangle of frequencies and investigate them for arbitrary parameter values except their special relations. Definitions of approaching and retiring areas of a singular point of system relatively to a family of line segments are formulated. Next, we investigate these areas bounds for singular points located in the triangle vertexes.