The different trajectories obtained from the May-Holling-Tanner predator-prey model via numerical solutions

Abstract

Studies of the population dynamics of interactions between species modeled by systems of differential equations can help in the development of future scenarios capable of assisting in decision-making processes, such as biological control. The purpose of this work was to investigate the possible trajectories obtained from the ordinary differential equations of the May-Holling-Tanner predator-prey model, using numerical methods. For this, the two-step Adams-Moulton predictor-corrector method was adopted. Simulations of three scenarios were carried out, each of them varying the parameters of the model in study. The results showed that the parameter values have a great impact on the evolution of the populations, providing different trajectory profiles in the phase plan and that the chosen numerical method made it possible to generate satisfactory solutions.