Analytical approach to a three species food chain model by applying Homotopy perturbation method

In this paper, a mathematical model is proposed and analyzed to study the effect of toxicant in a three species food chain system with “food limited” growth of prey population. The mathematical model is formulated using the system of non-linear ordinary differential equation. In the model, there are seven state variables, viz, prey population density, intermediate predator population density, top predator population density, toxicant concentration in the environment, toxicant concentration in the prey population, toxicant concentration in the intermediate predator population, toxicant concentration in the top predator population. Approximate analytical solutions for all above seven state variables are presented using Homotopy Perturbation Method (HPM) for all possible values of parameter. In addition, in this work the numerical simulation of the problem is also presented using MATLAB program to investigate the dynamic of the system. The same information also presented in graphical form which makes it easier to understand. A good agreement found between the analytical and the numerical solution.