Bifurcation Effects in a Degenerate Differential Model of Subpopulation Dynamics

The contribution is devoted to qualitative investigation of subpopulation dynamics, described by a degenerate differential model with basic logistic function. The research includes: finding stationary sets, such as isolated special points and stationary hyper-planes, investigation of their stability, complete classification of system phase portraits, complete classification of bifurcations in the system, determination of emergence condition. The main results of the qualitative analysis of the proposed model are represented in the form of theorems. Research results are illustrated with several graphs: system phase portraits and bifurcation diagrams. The illustrations demonstrate adequacy of qualitative results, obtained from the model simulation.