Before revision: We analyze some widespread models of population dynamics (logistic , \theta-logistic , and Gompertz model). In the first part of the article we discuss the deterministic versions of these models .
After revision: We analyze some widespread models of population dynamics (logistic , \theta-logistic stochastic differential equations, along with the exact expressions of both their probability density functions and their moments. We simulate in addition a few typical sample trajectories, and we provide a few examples of numerical computation of the said closed formulas at different noise intensities: this shows in particular that an increasing randomness - while making the process more unpredictable - asymptotically tends to suppress in average the logistic growth. These main results are preceded by a discussion of the noiseless, deterministic versions of these models .