Numerical simulations of a population dynamic model describing parasite destruction in a wild type pine forest

In order to investigate the behaviour of the resulting system, we will use numerical simulations, and we will introduce a parasite into a population of trees that: (1) is not oscillating around the positive equilibrium; (2) has some damped oscillations; (3) has some undamped oscillations. This will correspond to three scenarios for parameter values. As one may expect, this will lead to complex dynamics, since we combine the oscillations produced by the predator-prey system with the oscillations coming from the demographic properties of the prey.