Modeling and analysis of the survival of a biological species in a polluted environment: Effect of environmental tax

In this paper, a nonlinear dynamical model is proposed and analyzed to study the survival of biological species in a polluted environment considering the effect of environmental tax which can be used further to improve environmental quality. The environmental tax is imposed to control the emission of pollutants/toxicants only when the equilibrium concentration of pollutants go beyond its threshold level causing harm to the biological species and its ecosystem under consideration. Local and nonlinear stability conditions are obtained by considering suitable Liapunov function. Numerical simulation of the dynamical system is performed in order to illustrate the analytical findings. It is shown that the density of biological species decreases as the concentration of pollutants increases and may even become extinct if the concentration is very high. It has also been shown that the environmental tax plays an important role to control the concentration of pollutants in the atmosphere and maintaining the density of biological species at a desired level.