Abstract: By considering the influence of various uncertain noises, we established an uncertain Logistic population model with Allee effect, which was characterized by an uncertain differential equation. Firstly, we obtained the solution of the model, and discussed the stability of the equilibrium state. Secondly, the unknown parameters in the model were estimated by using the generalized moment estimation method under the framework of uncertainty theory. Finally, the parameter estimations of the model and the properties of the solution were explained by an example analysis.

Key words: Logistic population model, Allee effect, uncertain differential equation, parameter estimation, equilibrium state