A Numerical Study for Uncertainty in two Predators-One Prey Model

Abstract

In this article, a mathematical model had been presented, which delved into the dynamics of a system featuring two predators and one prey, characterized by a growth rate of the predator dependent on a specific ratio. When facing uncertain initial conditions in the model, it had become imperative to adapt the mathematical descriptions by treating these initial conditions as random variables governed by specific distribution functions. The beta distribution had been employed to represent the stochastic initial state of the two predators-one prey model, allowing for an examination of how the random initial state of the prey had impacted the dynamic behavior of the system. Given the lack of an analytical solution for the model, computer simulations had been resorted to in order to delve into the dynamics of the system. Consequently, various properties of the resulting numerical solution had been thoroughly discussed, shedding light on the intricacies of the system's behavior. In addition, the research had offered invaluable insights into understanding the impact of uncertainty on predator-prey interactions and the subsequent stability and behavior of the ecological system in uncertain conditions, further bolstered by the numerical results obtained.