In this paper, a non-linear system of differential equations is presented as a mathematical model to explain the interactions of three species in an ecosystem, which include prey, predator, and scavenger. The model takes into account the logistic growth of the prey population as well as the inter-species interactions. The paper uses local stability analysis to examine the system’s characteristics, including positivity, the boundedness of the solution, and the pre-requisites for the three populations’ stable coexistence. The existence of limit cycles in the positive quadrant, a crucial component of the dynamics of ecological systems, and the system’s persistence requirement are also examined in this work. The article also includes numerical simulations to support the theoretical study and provide a clearer picture of the ecosystem’s long-term dynamics.