On the Stability Analysis and Homotopy-Based Solution of three species Lotka-Volterra Model

The Lotka-Volterra model is a description of the dynamic behaviour of a multispecies number of competitors and/or predator-prey interactions which have found usefulness in non-linear control and simultaneous chemical engineering and other engineering fields. In this paper, we present the stability analysis and homotopy based solution of three species Lotka-Volterramodel. The three species Lotka-Volterra model equations have been considered and analysed. We performed the stability analysis of the equilibrium points and gave some qualitative information about the solution of the model equations through phase plane analysis. The Homotopy Analysis Method (HAM) has been used to solve the model and the results have been compared with other numerical solution and are found to be in good agreement. Finally, various simulations are done to discuss the solution.