Effects of industrialization and pollution on resource biomass: a mathematical model

Abstract

In this paper, a mathematical model is proposed and analyzed to study the depletion of resource biomass (plant/tree) due to industrialization and pollution. Industrialization dependent, constant, instantaneous, and periodic emissions of pollutant into the environment are taken into consideration. Criteria for local stability, instability, and global stability of non-negative equilibria are obtained. Numerical simulations are carried out to investigate the dynamics of the system. It is found that in the case of small periodic influx of pollutant into the environment, the resource biomass has a periodic behavior if the depletion rate coefficient of environmental pollutant is small. However, if this coefficient increases beyond a threshold value, then resource biomass converges towards its equilibrium.