Positive periodic solution for a stochastic non-autonomous enterprise cluster model

This paper investigates the dynamical behaviors for a stochastic non-autonomous enterprise cluster model. We will analyze how the parameters of the system and white noise affect the dynamical properties of the system. Using It $\hat{o}$'s formula, the comparison principle and inequality techniques, we study the existence, uniqueness, and extinction of nontrivial positive solutions. Particularly, we also study the existence of a stochastic positive periodic solution by using stochastic differential equation theory. Finally, two examples are introduced to verify the main results of this paper.