Effects of a Fluctuating Carrying Capacity on the Generalized Malthus-Verhulst Model

Figure 1

The plot of the mean value of 𝑥(𝑡) versus time in arbitrary units. The values of the parameters are 𝑥₀=1, 𝛾=0.2, 𝜎=0.5, 𝜇=1.9, 𝐾₀=13, and 𝑟=1. The analytical value of ⟨𝑥(𝑡)⟩ is given by (18). The agreement between the analytical expression (dashed line) and the numerical simulation (continuous line) is remarkable.