Abstract

In a real-world scenario, problems are identified, assumptions are made, data are collected and models are proposed. The underlying mathematical structure of the models is analyzed to appraise the sensitivity of the conclusions when the assumptions are not precisely met. In this work, we present the formulation of a modified Lotka-Volterra Predator-Prey Model to include terms which represent the degrees of internal competition of both predators and prey for their limited resources and a simulation of the stability behaviour of the resulting system. A computer simulation of the behaviour - stability of the solution of the model - of the system under different conditions is also presented. The critical points, eigenvalues and phase portrait of the system in terms of the model parameters are also obtained. The model interpretation and applicability are also discussed. The trajectories of the proposed model are not periodic and tend to equilibrium level with time, thus, making the system to be asymptotically stable. This behaviour is in line with the observable natural predator-prey system.

Keywords: Lotka-Volterra, Predictor-Prey Model, Simulation, Critical Points, Eigenvalues, and Stability