The Ratio Predator-Prey Model with Random Initial Conditions

In this work, the predator-prey model with the ratio-dependent functional response is considered,  where the randomness enters into the equations only through their initial conditions. It is done by assuming normal distribution as the initial states of the model to treat the randomness. The passage from the deterministic situation to the random one for these equations is also the most transparent. In addition, a numerical simulation will be offered using the modified approach founded on the fifth-order improved Runge-Kutta method. Furthermore, the stability of the equilibrium points, and certain statistical properties related to the random behaviour of predators and their prey, will be analyzed and discussed.