A stochastic model for dynamics of two populations and its stability

This paper presents a stochastic differential equation that models the alterations of two populations with respect to an immigration status. It is supposed that both populations experience positive birth and death rates and the immigration occurs in one direction from the first to the second population. Furthermore, the stability problem for the equilibrium states of the system is investigated. In addition, employing MATLAB programming, an example is provided in concern with the predictions of the growth rates of the populations during a decade