Stability and explicit stationary density of a stochastic single-species model

Abstract

Abstract This letter focus on the stability and explicit stationary density of a widely adopted stochastic single-species model. By taking advantage of Feller’s classification criteria, this letter verifies that there is a critical value Υ that characterizes the dynamical behaviors of the model, namely, if Υ\xa0>\xa00, then the model has a unique stationary probability distribution with an explicit density function; if Υ