A RESOURCE-DEPENDENT COMPETITION MODEL: EFFECTS OF POPULATION PRESSURE AUGMENTED INDUSTRIALIZATION

Abstract

In this paper, a nonlinear mathematical model is proposed and analyzed to study the effects of population pressure augmented industrialization on the survival of competing species dependent on resource. It is assumed that the growths of competing species are logistic and carrying capacities increase with increase in the density of resource biomass. Further, it is assumed that the resource biomass too is growing logistically in the environment and its carrying capacity decreases with the increase in densities of competing species and industrialization. The growth rate of population pressure is assumed to be proportional to the densities of competing species. Stabilities of all equilibria and conditions which influence the permanence of the system are carried out using theory of differential equations. Numerical simulations are performed to accomplish our analytical findings. It is shown that the equilibrium density of resource biomass decreases as (i) the growth rate coefficient of population pressure increases (ii) the growth rate coefficient of industrialization due to population pressure increases and (iii) the growth rate coefficient of industrialization due to resource biomass increases. It is found that the competitive outcome alters with increase in the growth rate coefficient of population pressure. Decrease in the equilibrium densities of competing species is also noted with increase in the growth rate coefficient of industrialization due to resource biomass.