THE MODEL OF PROTECTED POPULATION WITH COMPETITION AT A BILOCAL AREAL

Abstract

The authors use the apparatus of ordinary differential equations to study the issue of population dynamics of the protected species inhabiting a bilocal areal where there is a competition between the protected and unprotected parts of the population. In the protected and unprotected parts there is a competition between the members of the population, as well as the exchange between them. For the simulation of the evolutionary processes in the areal of protected populations, the authors used a system of two differential equations of the first order with respect to the population density in the protected and unprotected areas. The paper presents a qualitative study of the behaviour of the phase trajectories of the system of equations in a small neighbourhood around the singular points as equilibrium states of the system; the bifurcation parameters are identified. A case of continuously renewed population was analyzed in detail. The obtained results allows to create effective measures for the stable and sustainable existence of populations in protected and unprotected areas.

Keywords

• mathematical model, protected population, competition, bilocal area, singular points