Abstract: Volterra predator-prey mathematical model is of great significance to the study of the ecological relationship in population growths. By adding two populations to the Volterra predation model, a four species non-linear predatory mode where capture leads to intra-species competition is constructed and studied on. The model is analyzed qualitatively through Maple Software to describe the morphology of its phase diagram by means of numerical simulation and to discuss the stability of the model and its practical application.

Key words: Maple Software, predator-prey model, phase diagram, equilibrium point, stability, limit cycle