MODELLING THE MULTITEAM PREY–PREDATOR DYNAMICS USING THE DELAY DIFFERENTIAL EQUATION

Abstract

In nature, many species form teams and move in herds from one place to another. This helps them in reducing the risk of predation. Time delay caused by the age structure, maturation period, and feeding time is a major factor in real-time prey–predator dynamics that result in periodic solutions and the bifurcation phenomenon. This study analysed the behaviour of teamed-up prey populations against predation by using a mathematical model. The following variables were considered: the prey population Pr1, the prey population Pr2, and the predator population Pr3. The interior equilibrium point was calculated. A local satiability analysis was performed to ensure a feasible interior equilibrium. The effect of the delay parameter on the dynamics was examined. A Hopf bifurcation was noted when the delay parameter crossed the critical value. Direction analysis was performed using the centre manifold theorem. The graphs of analytical results were plotted using MATLAB.