Abstract

Acid lowers the pH levels in water bodies below what is required for survival of aquatic life and increases the toxicity of metals. For this effect, a mathematical model has been proposed using a system of non-linear ordinary differential equations with four state variables. The dependent variables are amount of acid and metal in water, density of favorable resources (phytoplankton), density of fish population and nutrient concentration under the assumption that the amount of metal present in water is less than the amount of acid present in water. Conditions for local stability and feasible equilibrium points have been determined. Nonlinear stability analysis of the non-trivial equilibrium points has been discussed and it was found that system of the differential equations show more feasible results if the crowding effect is incorporated for fish population. Further it was also observed that, nutrients play important role for the growth and survival of the species. Conditions for the existence of the equilibrium points have been drawn and the criteria for the survival or the extinction of the species have been obtained using numerical simulation. Stability of the system is explained analytically as well as graphically.

Authors and Affiliations