PHASE PORTRAIT OF A DIFFERENTIAL EQUATIONS SYSTEM MODELING COMPETITIVE INTERACTION // BSU Bulletin. Mathematics, Informatics. - 2023. №3. . - С. 3-13.

PHASE PORTRAIT OF A DIFFERENTIAL EQUATIONS SYSTEM MODELING COMPETITIVE INTERACTION

DOI: 10.18101/2304-5728-2023-3-3-13 UDK: 517.925.5

The 6-parametric family of 3-dimentional autonomous ordinary differen- tial 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 trian- gle of frequencies and investigate them for arbitrary parameter values except their spe- cial relations. Definitions of approaching and retiring areas of a singular point of sys- tem relatively to a family of line segments are formulated. Next, we investigate these areas bounds for singular points located in the triangle vertexes.

аutonomous system, ordinary differential equations, parametric family of systems, 3-dimentional system, dynamic model, singular points, phase portrait, invariant set, numeric example.