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

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摘要

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.

论文关键词:Stochastic population model,Explicit stationary density,Stability

论文评审过程:Received 15 July 2020, Revised 27 July 2020, Accepted 2 August 2020, Available online 25 August 2020, Version of Record 25 August 2020.

论文官网地址:https://doi.org/10.1016/j.amc.2020.125593