Nonlinear models for the survival of two competing species dependent on resource in industrial environments

Abstract

In this paper, a nonlinear mathematical model is proposed and analysed to study the survival of two competing species dependent on resource in industrial environments with and without diffusion. The competing species are assumed to be either partially dependent, wholly dependent or predating on the resource. A corresponding conservation model is also proposed and analysed to study the importance of regeneration of the exploited resource as well as the control of industrialization. In the case of without diffusion, criteria for survival and extinction of competing species are derived and equilibrium levels of the resource biomass, competing species and industrialization density are compared. In the case of diffusion, it is shown that solutions of the system approach to the steady state more rapidly with the increase in diffusion coefficients. By analysing the conservation model it is shown that if suitable efforts are made to conserve the resource biomass and to control the undesired level of industrialization pressure, an appropriate level of resource biomass density can be maintained and thus the survival of species may be ensured.