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

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 > 0, then the model has a unique stationary probability distribution with an explicit density function; if Υ < 0, then the trivial solution of the model is stochastically asymptotically stable. These findings complement the results of some previous investigations. This letter also makes use of these theoretical findings to dissect the growth of African Wild Dogs and malignant tumors models.