(untitled) (European Journal of Pure and Applied Mathematics, 2025)
In this paper, we introduce a novel competitive stochastic predator-prey model by means of Holling type II with small random immigration. A Series of analytical results are conducted on the model such as the boundedness of the model’s solution, stochastic mean square stability, and the conditions of the persistence and extinction of the predator-prey population. All analytical results were validated with numerical simulations by choosing different sets of small random immigration. Conditions on the random immigration under which the system is stochastically stable are specified. In addition, small immigration has been shown to have a great impact on persistence and extinction of the system, which can play an important role in species conservation, especially by controlling the conditions of stochastic small immigration.